Celtic increased their lead at the top of the Scottish Premier League to seven points with a win at Dens Park.
The visitors' first-half domination only resulted in one goal, an excellent Georgios Samaras overhead kick from 10 yards.
Dundee were lively after the break, with Fraser Forster clawing Colin Nish's header off the line.
But a classy bit of control and lob by Gary Hooper, after Lustig's long ball, sealed victory over bottom club Dundee.
Celtic went into this one looking to extend the gap between themselves and nearest challengers Inverness and Motherwell and get their fifth league win on the trot.
Dundee's aim was to narrow the concerning nine point gap between themselves at the foot of the table and Ross County in 11th.
It was an encouraging start for the home support at Dens Park, then, to see Stephen O'Donnell fire in the first real shot on target.
Victor Wanyama flashes a shot past Kyle Benedictus and over the bar
The midfielder benefited from poor control by Victor Wanyama on the edge of the box, but his effort went over the bar.
After 10 minutes Celtic began to assert their authority and Charlie Mulgrew's corner kicks were their weapon of choice.
Efe Ambrose got his knee on the first of Mulgrew's left-footed deliveries, but the unorthodox attempt came back off the bar and Wanyama drove the rebound over.
However, another one of Mulgrew's set-pieces was the catalyst in the visitors taking a 16th minute lead.
Again, it was hit left-footed from the right side and Tony Watt's side-foot volley from a tight angle at the back post forced Rab Douglas into a close-range save.
But that block saw the ball loop to Samaras, whose expert overhead kick from 10 yards found the roof of the net despite a desperate attempt by Jim McAlister to head off the line - a fine way for the Greek to score his eighth goal of the season.
The striker could have made it nine for the season shortly after when Beram Kayal put him through at the corner of the box, but Douglas touched his curling shot round the far post to prevent Celtic doubling their lead.
Dundee struggled to gain a foot-hold in the game throughout the rest of the first half and manager Barry Smith would have been pleased the deficit remained at one goal.
Ambrose did threaten once more just before referee Iain Brines blew for the interval, surging from midfield to arrow a right-footed shot Douglas's way from 25 yards, but the keeper was equal to it.
Celtic re-emerged for the second half with Lustig replacing Mulgrew, who had damaged a rib.
Perhaps it was the relief at Mulgrew's absence that boosted Dundee at the beginning of the second half.
McAlister linked intelligently with Nish on the right before sending in a shot which Wanyama deflected wide.
Ryan Conroy could not force anything from the resultant corner, but he was soon scampering down the left creating havoc.
His excellent cross was met by Nish, whose near-post header seemed destined to ripple the back of the net before the hand of Forster clawed it away - easily the home side's best chance.
Spurred on, John Baird then went very close again with a shot from the edge of the box on 55 minutes which Emilio Izaguirre slid in desperately to divert away from goal.
Lustig soon showed his attacking prowess by swinging in a low ball which came off Kyle Benedictus and required excellent reactions from Douglas.
The Swedish right-back then set-up Hooper to double Celtic's lead on 71 minutes.
Lustig's long-ball should have been dealt with, but Hooper raced clear of Benedictus and Declan Gallagher to show an exquisite first touch and lob over Douglas from just inside the box.
Almost immediately, another Nish header forced Forster to tip over to deny Dundee a quick reply.
Scott Brown, ever lively, angled a pass to set Hooper up again on 80 minutes, but the Englishman narrowly missed the target.
Douglas did well to deny Hooper again late-on and despite a couple of Dundee corners causing some confusion in the box, Celtic made it to the final whistle with a clean sheet.
Gary Hooper takes a shot. Fantastic save by Rab Douglas.
Ryan Conroy takes a inswinging corner to the near post, clearance by Mikael Lustig.
The assistant referee flags for offside against Mark Stewart. Fraser Forster restarts play with the free kick.
Substitution Stephen O'Donnell leaves the field to be replaced by Martin Boyle.
James McAlister challenges Patrick McCourt unfairly and gives away a free kick. Patrick McCourt delivers the ball from the free kick right-footed from right channel.
Mikael Lustig challenges Mark Stewart unfairly and gives away a free kick. Matthew Lockwood takes the free kick.
Substitution Patrick McCourt joins the action as a substitute, replacing Tony Watt.
Centre by Mikael Lustig.
Direct free kick taken by Fraser Forster.
Substitution Mark Stewart replaces John Baird.
Inswinging corner taken by Ryan Conroy from the right by-line, clearance made by Kelvin Wilson. Inswinging corner taken by James McAlister, Kyle Benedictus concedes a free kick for a foul on Fraser Forster.
Assist by Mikael Lustig.
70:36 Goal scored
Goal! - Gary Hooper - Dundee 0 - 2 Celtic Goal scored by Gary Hooper from inside the box low into the middle of the goal. Dundee 0-2 Celtic.
Free kick crossed right-footed by Scott Brown, clearance by Stephen O'Donnell.
Booking Gary Hooper receives a yellow card.
Booking Booking for Kyle Benedictus.
Free kick awarded for an unfair challenge on Gary Hooper by Kyle Benedictus.
Unfair challenge on Stephen O'Donnell by Gary Hooper results in a free kick. Direct free kick taken by Kyle Benedictus.
Unfair challenge on Stephen O'Donnell by Emilio Izaguirre results in a free kick. Stephen O'Donnell takes the direct free kick.
Substitution James Forrest replaces Beram Kayal.
Corner taken right-footed by James McAlister to the near post, Mikael Lustig makes a clearance.
The assistant referee flags for offside against Ryan Conroy. Indirect free kick taken by Kelvin Wilson.
Inswinging corner taken left-footed by Ryan Conroy.
John Baird fouled by Efe Ambrose, the ref awards a free kick. Free kick crossed by Ryan Conroy, Efe Ambrose manages to make a clearance. Kevin McBride has an effort at goal from long distance that goes wide left of the target.
Colin Nish takes a shot. Fantastic save by Fraser Forster.
Corner taken by Ryan Conroy from the right by-line to the near post, clearance made by Efe Ambrose.
Foul by Scott Brown on Matthew Lockwood, free kick awarded. Rab Douglas takes the free kick.
The game restarts for the second half.
Substitution (Celtic) makes a substitution, with Mikael Lustig coming on for Charlie Mulgrew.
45:00 +1:06 Half time
Half Time The match has reached half-time.
Efe Ambrose takes a shot. Brilliant save by Rab Douglas.
Free kick awarded for an unfair challenge on Ryan Conroy by Tony Watt. Direct free kick taken by Matthew Lockwood.
Tony Watt concedes a free kick for a foul on Matthew Lockwood. Matthew Lockwood takes the direct free kick.
Stephen O'Donnell challenges Victor Wanyama unfairly and gives away a free kick. Kelvin Wilson restarts play with the free kick.
The ball is sent over by Emilio Izaguirre.
Ryan Conroy takes a corner.
The ball is delivered by Emilio Izaguirre, clearance by Matthew Lockwood.
Matthew Lockwood challenges Tony Watt unfairly and gives away a free kick. Charlie Mulgrew takes the direct free kick. The referee blows for offside against Victor Wanyama. Rab Douglas restarts play with the free kick.
Emilio Izaguirre produces a cross.
Georgios Samaras takes a shot. Save by Fraser Forster. Corner taken by Charlie Mulgrew from the right by-line to the near post, Declan Gallagher manages to make a clearance.
Corner taken left-footed by Charlie Mulgrew to the near post.
Gary Irvine concedes a free kick for a foul on Tony Watt. Free kick crossed left-footed by Charlie Mulgrew, Matthew Lockwood makes a clearance.
Tony Watt provided the assist for the goal. Tony Watt takes a shot. Rab Douglas makes a save.
15:58 Goal scored
Goal! - Georgios Samaras - Dundee 0 - 1 Celtic Georgios Samaras finds the net with a goal from deep inside the penalty box high into the middle of the goal. Dundee 0-1 Celtic.
Inswinging corner taken by Charlie Mulgrew from the right by-line, James McAlister makes a clearance. Corner taken by Charlie Mulgrew from the right by-line,
Long range shot from Gary Hooper misses to the left of the target.
Corner taken by Charlie Mulgrew.
Shot by Stephen O'Donnell from outside the area goes high over the crossbar.
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