While Chelsea lacked fluency in attack and were often careless in defence, the hosts played with the sort of passion and drive they demonstrated in their last home game, a 1-0 win over Manchester City.
Driven by the classy Pienaar and the enthusiasm and endless running of Donovan and Tim Cahill, Everton dominated in midfield and their opener owed much to their harrying of Chelsea.
Jose Bosingwa's sloppy throw-in was intercepted by Pienaar, who continued his run towards goal and gleefully fired the ball into the roof of the net after Frank Lampard's challenge on Cahill deflected the ball into the South African's path.
The visitors did settle midway through the first period and had a 15-minute spell in which they dominated possession and played with a cohesion lacking for the rest of the afternoon.
Juan Mata twice set up excellent chances after sneaking free on the Everton right and pulling the ball back to onrushing colleagues.
But Daniel Sturridge was unlucky to see his strike deflected narrowly over by Phil Neville, and Lampard - back in the side and named as skipper after four weeks out with a calf injury - dragged the second opportunity well wide with his left foot.
Everton continued to look comfortable after the interval as Chelsea barely mustered a noteworthy change against a perfectly organised rearguard.
As the game wore on Everton began to drop back further towards their goal, but the Londoners still failed to threaten.
“Everton had a dream start, got in Chelsea's faces and played with energy and organisation. Chelsea huffed and puffed, struggled to create clearcut chances after the break and Everton were good value for their win”
Steve BowerBBC Match of the Day commentator
The hosts sealed their straight home Premier League win over Chelsea 19 minutes from time - and ensured they scored twice in a game for the first time in 13 matches - courtesy of Stracqualursi.
It stemmed from a crunching tackle on the halfway line by Neville which epitomised Everton's spirit, energy and quality.
A sweeping team move began when Neville slid in on Ashley Cole, who subsequently hobbled off injured, and allowed Donovan to beat David Luiz and cleverly slip the ball through for Stracqualursi to beat Petr Cech.
Everton manager David Moyes:
"Recently we have done very well but today capped it. We played well, it was hard and Chelsea were good but we did what we do at Goodison. We are hard to beat.
"It was a great start and a great start for Steven Pienaar coming back and scoring. Chelsea came into it and had one or two chances and we had to ride our luck a little bit but we kept at it, got to half-time and got the second goal in the second half.
"We blocked and defended well and did all the things you hoped you would do. Great credit to the players, they are beginning to show what they are about. They are beginning to find the form they are capable of, and I think we can play much better and I am looking forward to that.
"Denis was terrific today. He is an old-fashioned centre-forward with a bit of hustle and bustle about him and earned his goal. But the best part of it was tackle by Phil Neville. I was nearly cheering Phil's tackle as much as the goal."
Chelsea manager Andre Villas-Boas:
"It was one of our worst displays of the season - if not the worst. Today we couldn't be ourselves and express our football and we ended up heavily defeated.
Villas-Boas accepts blame for Chelsea defeat at Everton
"We saw a very, very brave Everton that showed their aggressiveness and showed great commitment to win.
"Our players showed exactly that and, if there is one defeat that the manager should take the blame, it is this one so I will go back to my pre-planning and decision-making because maybe it wasn't right to help the players.
"Everton's pressure really was hard on our back four and we spoke about it but it should be addressed by me.
"One of the things we always have is that we manage to create opportunities and this wasn't the case today. We fell very short in terms of goalscoring opportunities when a response was needed."
Full Time The game is over, as the referee blows his whistle.
Free kick taken by Branislav Ivanovic.
90:00 +2:48 Substitution
Substitution (Everton) makes a substitution, with Shane Duffy coming on for Denis Stracqualursi.
Unfair challenge on Branislav Ivanovic by Tim Cahill results in a free kick.
Inswinging corner taken right-footed by Frank Lampard from the left by-line, Denis Stracqualursi manages to make a clearance.
Free kick awarded for an unfair challenge on Royston Drenthe by Jose Bosingwa. Royston Drenthe restarts play with the free kick.
Tim Cahill takes a shot. Blocked by Branislav Ivanovic.
Royston Drenthe takes the direct free kick.
Substitution Tony Hibbert replaces Darron Gibson.
Free kick awarded for an unfair challenge on Royston Drenthe by Florent Malouda.
The referee gives a free kick against Royston Drenthe for handball. Direct free kick taken by Frank Lampard.
David Luiz fouled by Marouane Fellaini, the ref awards a free kick. Frank Lampard takes the direct free kick.
Free kick awarded for a foul by Leighton Baines on Frank Lampard. Raul Meireles takes the free kick.
Romelu Lukaku takes a shot. Save by Tim Howard.
Unfair challenge on Fernando Torres by Johnny Heitinga results in a free kick. Free kick taken by Raul Meireles.
Marouane Fellaini challenges Raul Meireles unfairly and gives away a free kick. David Luiz takes the direct free kick.
Substitution Juan Mata leaves the field to be replaced by Romelu Lukaku.
Substitution (Chelsea) makes a substitution, with Ryan Bertrand coming on for Ashley Cole.
Substitution Royston Drenthe comes on in place of Steven Pienaar.
Landon Donovan provided the assist for the goal.
70:55 Goal scored
Goal - Denis Stracqualursi - Everton 2 - 0 Chelsea Goal scored by Denis Stracqualursi from deep inside the penalty area to the bottom right corner of the goal. Everton 2-0 Chelsea.
Substitution (Chelsea) makes a substitution, with Florent Malouda coming on for Michael Essien.
Unfair challenge on Jose Bosingwa by Leighton Baines results in a free kick. Direct free kick taken by Jose Bosingwa.
Fernando Torres takes a shot. Tim Howard makes a save.
Tim Cahill gives away a free kick for an unfair challenge on Branislav Ivanovic. Free kick taken by Raul Meireles.
Denis Stracqualursi takes a shot. Save by Petr Cech.
Leighton Baines takes the free kick.
Booking Fernando Torres receives a caution for unsporting behaviour.
Foul by Fernando Torres on Steven Pienaar, free kick awarded.
Denis Stracqualursi takes a shot. Blocked by Branislav Ivanovic.
Foul by David Luiz on Denis Stracqualursi, free kick awarded. Phil Neville takes the free kick.
The assistant referee signals for offside against Denis Stracqualursi. Raul Meireles takes the direct free kick.
Ashley Cole is adjudged to have handled the ball. Phil Neville takes the free kick.
The free kick is swung in left-footed by Leighton Baines, Ashley Cole gets a block in. Landon Donovan takes a outswinging corner from the right by-line to the near post.
Booking Jose Bosingwa is given a yellow card.
Free kick awarded for an unfair challenge on Steven Pienaar by Jose Bosingwa.
The referee gives a free kick against Marouane Fellaini for handball. Frank Lampard takes the direct free kick.
Foul by Tim Cahill on David Luiz, free kick awarded. Raul Meireles takes the direct free kick.
Tim Cahill is flagged offside by the assistant referee. Raul Meireles takes the free kick.
Fernando Torres challenges Leighton Baines unfairly and gives away a free kick. Sylvain Distin takes the direct free kick.
Shot by Marouane Fellaini. Frank Lampard gets a block in.
The match restarts for the second half.
45:00 +1:02 Half time
Half Time The first half comes to an end.
Fernando Torres takes a shot. Save made by Tim Howard.
Free kick awarded for an unfair challenge on Denis Stracqualursi by David Luiz. Direct free kick taken by Johnny Heitinga.
Denis Stracqualursi takes a shot. Save by Petr Cech.
Direct free kick taken by Johnny Heitinga.
Booking The referee shows Raul Meireles a yellow card for unsporting behaviour.
Denis Stracqualursi fouled by Raul Meireles, the ref awards a free kick.
Branislav Ivanovic challenges Denis Stracqualursi unfairly and gives away a free kick. Johnny Heitinga takes the free kick.
Free kick awarded for a foul by Landon Donovan on Raul Meireles. Raul Meireles takes the free kick.
Unfair challenge on Denis Stracqualursi by David Luiz results in a free kick. The free kick is swung in left-footed by Leighton Baines. The assistant referee flags for offside against Tim Cahill. Indirect free kick taken by Petr Cech.
Foul by Marouane Fellaini on Juan Mata, free kick awarded. Free kick crossed left-footed by Juan Mata from right wing, clearance made by Darron Gibson.
Phil Neville gives away a free kick for an unfair challenge on Juan Mata. Free kick taken by David Luiz.
Tim Cahill is ruled offside. Petr Cech restarts play with the free kick.
Unfair challenge on Steven Pienaar by Michael Essien results in a free kick. Johnny Heitinga restarts play with the free kick.
Effort from the edge of the area by Frank Lampard goes wide of the right-hand upright.
Shot by Daniel Sturridge. Phil Neville gets a block in. Juan Mata takes the inswinging corner, clearance made by Tim Cahill.
Fernando Torres takes a shot. Phil Neville gets a block in. Corner taken by Juan Mata from the left by-line, Tim Cahill manages to make a clearance. Michael Essien takes a shot. Blocked by Phil Neville.
Unfair challenge on David Luiz by Denis Stracqualursi results in a free kick. Direct free kick taken by Petr Cech.
Juan Mata takes the inswinging corner, Tim Cahill manages to make a clearance. Foul by Fernando Torres on Johnny Heitinga, free kick awarded. Tim Howard restarts play with the free kick.
Phil Neville gives away a free kick for an unfair challenge on Daniel Sturridge. Direct effort from the free kick comes in from Frank Lampard.
Corner taken by Leighton Baines played to the near post, clearance by Frank Lampard.
Landon Donovan takes a shot. Petr Cech makes a save.
Tim Cahill is caught offside. Jose Bosingwa takes the direct free kick.
Headed effort from inside the penalty area by Denis Stracqualursi misses to the right of the target.
The offside flag is raised against Denis Stracqualursi. David Luiz takes the direct free kick.
4:47 Goal scored
Goal - Steven Pienaar - Everton 1 - 0 Chelsea Steven Pienaar scores a goal from inside the box to the top left corner of the goal. Everton 1-0 Chelsea.
The referee gives a free kick against Marouane Fellaini for handball. Petr Cech takes the direct free kick.
The assistant referee signals for offside against Ashley Cole. Johnny Heitinga restarts play with the free kick.
Landon Donovan produces a right-footed shot from just outside the box that misses to the right of the target.
Landon Donovan has an effort at goal from just outside the box which goes wide of the right-hand upright.
The referee gets the game started.
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