Suarez, who returned to the first team in the League Cup this week after his 10-match ban for biting Branislav Ivanovic, put the Reds 2-0 up with a tap-in from Daniel Sturridge’s superb run and cross, and restored their two-goal lead late on from an almost identical move.
The excellent Sturridge had earlier put Liverpool ahead with a handball goal, missed by the officials, that was almost certainly accidental but should not have stood in any case.
Sunderland, with Kevin Ball in charge following Paolo Di Canio’s sacking, played well throughout, with Sebastian Larsson hitting the bar with a free-kick, and they pulled one back when Emanuele Giaccherini pounced after ex-Black Cats keeper Simon Mignolet failed to hold Ki Sung-yeung’s drive.
But Suarez’s second, which came on the break as the hosts piled men forward in search for an equaliser, put the match to bed, and sent Liverpool joint-second.
Despite an encouraging performance, Sunderland remain rooted to the bottom of the division with just one point in six matches.
Pre-match: Luis Suarez heads a triple-pronged Liverpool attack in the absence of Philippe Coutinho, while Daniel Agger returns to the bench from injury; caretaker Sunderland boss Kevin Ball is cheered by the fans as Lee Cattermole returns to the starting XI in the post-Di Canio era.
24’ – WOODWORK: Larsson rattles the crossbar with a fantastic free-kick.
28’ – GOAL (Sunderland 0-1 Liverpool): Sturridge appears to head home Gerrard’s corner, but replays show it struck his arm.
36’ - GOAL (Sunderland 0-2 Liverpool): Suarez signals his return to Premier League action with a tap-in after great work from Sturridge, who left Carlos Cuellar for dead before playing the cut-back.
43’ – SAVE: Mignolet denies his former team-mate Craig Gardner with a great one-on-one stop.
52’ – GOAL (Sunderland 1-2 Liverpool): Ki’s long shot is saved by Mignolet, but he can only palm it into Giaccherini’s path for a simple finish.
66+67’ – CHANCES: Victor Moses twice goes close with excellent efforts from range, one saved by Kieren Westwood, the other bouncing inches wide.
88’ – GOAL (Sunderland 1-3 Liverpool): Suarez kills the game with a clinical first-time finish after more excellent work out wide by Sturridge.
Liverpool’s Victor Moses made his 100th Premier League appearance.
The Reds are unbeaten in seven Premier League games away from Anfield (W4 D2), last losing on the road in March to Southampton.
Sunderland have won only three of their 25 Premier League games against Liverpool.
Sunderland haven’t kept a clean sheet in their last 10 Premier League games.
If it was Luis Suarez… Sturridge’s handball goal was most probably accidentally, and he possibly did not even realise it had come off his arm. But if it was Suarez, there would have been uproar. Reputations precede players.
MAN OF THE MATCH
Daniel Sturridge (Liverpool): A Suarez-esque performance from the England forward, complete with a handball goal and two glorious assists.
Sunderland: Westwood 6, Gardner 6, Colback 6, O'Shea 6, Cuellar 5, Larsson 7, Ki 6, Cattermole 6, Johnson 7, Giaccherini 7, Altidore 6. Subs: Celustka 6, Mavrias NA
Liverpool: Mignolet 6, Toure 7, Sakho 6, Skrtel 7, Enrique 6, Henderson 6, Lucas 6, Gerrard 6, Moses 7, Suarez 8, Sturridge 8. Subs: Sterling 6
THE MATCH IN A TWEET