Reds striker Fabio Borini had two early shots saved before Steven Fletcher tapped in for Sunderland after Craig Gardner's mazy run and cross.
Liverpool came close to a goal when Glen Johnson's shot hit the crossbar and Steven Gerrard fired just wide.
Liverpool deserved draw - O'Neill
The equaliser eventually came when Luis Suarez sidefooted in after his initial effort came back off Titus Bramble.
Jonjo Shelvey had a late chance for the visitors as they finished the match the stronger but his shot was saved by keeper Simon Mignolet.
The build-up to the match had been dominated by the Hillsborough findings and there was a show of solidarity between the two clubs at the ground, Sunderland flying flags at the Stadium of Light at half-mast as a mark of respect.
Once the match got under way, the Black Cats initially highlighted a lack of creativity and cutting edge from the Reds.
The home side allowed their guests plenty of possession and tried to catch them out on the break as they put up a disciplined defensive barrier.
The strategy almost had to be abandoned early on when defender Carlos Cuellar's tame header back to Mignolet let in Borini, whose shot was blocked by the Black Cats keeper.
Borini had another opening when Suarez touched the ball into his path only for the Italian's first-time shot to be parried away by the alert Mignolet.
But, in the main, Sunderland kept Liverpool comfortably at arm's length and they reaped the rewards when they took the lead with their first real attack.
Steve BowerBBC Match of the Day commentator
"The two Irish managers share the spoils. Luis Suarez got the goal as Liverpool came from behind to get the equaliser to Steve Fletcher's goal for Sunderland. But Brendan Rodgers still has to wait for his first league win as Liverpool manager. It's also more than 100 years since Liverpool failed to win one of their first four league games of a season."
Gardner weaved past Suarez and Johnson before sliding a low cross for Fletcher to slot in on his home Premier League debut.
To add to Liverpool's growing frustrations, Suarez was booked for diving when he went over John O'Shea's leg.
The Reds regrouped after the break and Johnson, playing at left-back, cut inside before curling in a shot that came back off the crossbar.
Sunderland survived another scare when Raheem Sterling's cross caused confusion in their area, ending with Gerrard's guided shot hitting the outside of the post.
Teenager Sterling was Liverpool's main threat and it was another of his crosses from the right that led to the equaliser.
Suarez failed to connect properly with his first attempt and, after the ball ricocheted back to him off Bramble, he steered in a shot with his left foot.
Shelvey's failure to take his late chance left both camps with a point and still without a Premier League win so far this season.
Sunderland boss Martin O'Neill:
"I thought we played well in the first half, we gave as good as we got, got the goal in front.
Liverpool deserved win - Rodgers
"The irony of it is that we were probably in the second half having our best spell in possession of the ball and looked as if we had got a second wind when they got the equalising goal.
"But they had a number of chances and didn't take them, hit the bar and so from that viewpoint, probably a point was a fair result."
Liverpool manager Brendan Rodgers:
"The players have been terrific. It's been a difficult week, of course, as you can imagine for the city and everything surrounding it.
"The performance was outstanding, both our creativity and our movement, and there was a really good tempo and rhythm to our game.
"We went behind and we were disappointed with the goal, it was a soft goal from our perspective and it went in against the run of play.
"But in the second half, we showed a real reaction and continued what we were doing in the first half, but really upped the tempo and the penetration in our game and by the end of it, I am sure Sunderland were probably happier with the point than ourselves."
Full Time The final whistle is blown by the referee.
Corner taken by Stewart Downing from the left by-line, Headed effort from inside the area by Glen Johnson misses to the right of the target.
Foul by Stephane Sessegnon on Glen Johnson, free kick awarded. Free kick taken by Jose Reina.
Louis Saha has a shot on goal from outside the box which misses left.
Raheem Sterling gives away a free kick for an unfair challenge on Fraizer Campbell. Simon Mignolet takes the direct free kick.
Raheem Sterling fouled by Stephane Sessegnon, the ref awards a free kick. Free kick crossed right-footed by Steven Gerrard from left wing, clearance made by Fraizer Campbell.
Glen Johnson takes the direct free kick.
Substitution Steven Fletcher leaves the field to be replaced by Louis Saha.
Raheem Sterling fouled by Craig Gardner, the ref awards a free kick.
Unfair challenge on Steven Gerrard by Sebastian Larsson results in a free kick. Free kick taken by Steven Gerrard.
Steven Gerrard takes the free kick.
Booking Sebastian Larsson goes into the book for unsporting behaviour.
Sebastian Larsson concedes a free kick for a foul on Raheem Sterling.
Luis Suarez takes a shot. Save made by Simon Mignolet. Header from deep inside the penalty area by Luis Suarez goes harmlessly over the crossbar.
Corner taken right-footed by Luis Suarez.
Stewart Downing decides to take a short corner.
Outswinging corner taken by Stewart Downing from the left by-line played to the near post, clearance by Craig Gardner.
James McClean concedes a free kick for a foul on Martin Kelly. Direct free kick taken by Steven Gerrard.
Substitution Danny Rose leaves the field to be replaced by Fraizer Campbell.
The assist for the goal came from Raheem Sterling.
70:25 Goal scored
Goal - Luis Suarez - Sunderland 1 - 1 Liverpool A goal is scored by Luis Suarez from close in low into the middle of the goal. Sunderland 1-1 Liverpool.
Effort on goal by Glen Johnson from just outside the penalty area goes harmlessly over the target.
Craig Gardner takes a shot. Blocked by Daniel Agger.
Stephane Sessegnon takes a shot. Raheem Sterling has an effort at goal from outside the penalty box missing to the wide left of the goal. Martin Skrtel gets a block in.
Steven Gerrard takes a shot. Martin Skrtel takes a shot. Comfortable save by Simon Mignolet. Blocked by Martin Skrtel.
Outswinging corner taken left-footed by Stewart Downing from the left by-line.
Substitution Stewart Downing replaces Fabio Borini.
Titus Bramble takes the direct free kick.
Booking Martin Skrtel goes into the referee's book.
Unfair challenge on Stephane Sessegnon by Martin Skrtel results in a free kick.
Foul by Danny Rose on Raheem Sterling, free kick awarded. Indirect free kick taken by Jose Reina.
Steven Gerrard produces a right-footed shot from just outside the box that hits the post.
Effort from outside the penalty area by Craig Gardner goes wide left of the target.
Shot from just outside the box by Jack Colback goes over the bar.
The referee blows for offside against Steven Fletcher. Jose Reina takes the free kick.
Corner from the left by-line taken by Jack Colback, clearance made by Martin Skrtel. Craig Gardner takes a shot. Blocked by Martin Kelly.
Foul by John O'Shea on Luis Suarez, free kick awarded. Free kick crossed by Steven Gerrard, John O'Shea manages to make a clearance.
Header by Fabio Borini from deep inside the penalty area misses to the left of the target.
Glen Johnson produces a curled right-footed shot from 20 yards.
Free kick awarded for a foul by Stephane Sessegnon on Joe Allen. Joe Allen takes the direct free kick.
The ball is swung over by Glen Johnson.
Luis Suarez fouled by Sebastian Larsson, the ref awards a free kick. Direct free kick taken by Joe Allen.
Corner taken right-footed by Steven Gerrard, clearance made by Steven Fletcher.
Jonjo Shelvey takes a shot. Save by Simon Mignolet.
The second half has started.
Substitution (Sunderland) makes a substitution, with Titus Bramble coming on for Carlos Cuellar.
45:00 +1:07 Half time
Half Time The half-time whistle blows.
Martin Skrtel concedes a free kick for a foul on Steven Fletcher. Simon Mignolet takes the free kick.
Free kick awarded for a foul by Jack Colback on Glen Johnson. Free kick taken by Glen Johnson.
Jonjo Shelvey challenges Lee Cattermole unfairly and gives away a free kick. Free kick taken by John O'Shea.
Craig Gardner challenges Luis Suarez unfairly and gives away a free kick. Direct free kick taken by Glen Johnson.
Danny Rose fouled by Jonjo Shelvey, the ref awards a free kick. Indirect free kick taken by Simon Mignolet.
The offside flag is raised against Raheem Sterling. Danny Rose takes the direct free kick.
Booking Booking for Luis Suarez for unsporting behaviour.
Free kick awarded for an unfair challenge on Raheem Sterling by Danny Rose. Free kick taken by Jose Reina.
Corner from right by-line taken by Steven Gerrard.
Danny Rose challenges Raheem Sterling unfairly and gives away a free kick. Shot comes in from Luis Suarez from the free kick.
Free kick awarded for an unfair challenge on Fabio Borini by Jack Colback. Jose Reina takes the direct free kick.
Inswinging corner taken by Jack Colback.
Craig Gardner provided the assist for the goal.
28:50 Goal scored
Goal - Steven Fletcher - Sunderland 1 - 0 Liverpool Goal scored by Steven Fletcher from close range low into the middle of the goal. Sunderland 1-0 Liverpool.
Shot from just outside the area by Steven Gerrard goes over the bar.
Raheem Sterling takes a shot. Craig Gardner gets a block in.
Fabio Borini takes a shot. Save by Simon Mignolet.
Danny Rose gives away a free kick for an unfair challenge on Raheem Sterling. The free kick is delivered right-footed by Steven Gerrard from right wing, clearance made by Steven Fletcher.
Foul by Jack Colback on Steven Gerrard, free kick awarded. Martin Skrtel takes the free kick.
Jonjo Shelvey has an effort at goal from the edge of the box that misses to the right of the target. Daniel Agger concedes a free kick for a foul on Stephane Sessegnon. Free kick crossed right-footed by Sebastian Larsson.
Fabio Borini takes a shot. Simon Mignolet makes a save.
The ball is swung over by Fabio Borini, save by Simon Mignolet.
Shot from just outside the box by Luis Suarez misses to the left of the goal.
Foul by Lee Cattermole on Fabio Borini, free kick awarded. Steven Gerrard restarts play with the free kick.
Danny Rose fouled by Martin Kelly, the ref awards a free kick. Free kick taken by Danny Rose.
Martin Kelly gives away a free kick for an unfair challenge on James McClean. Free kick taken by Danny Rose.
Craig Gardner fouled by Martin Kelly, the ref awards a free kick. Simon Mignolet takes the free kick.
Long distance shot from Jonjo Shelvey misses to the left of the goal.
Free kick awarded for an unfair challenge on Danny Rose by Martin Kelly. Free kick taken by Danny Rose.
The ref blows the whistle to start the match.
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