The Uruguay striker - banned for 10 matches for a bite on Chelsea defender Branislav Ivanovic in April - seemed to do everything but score as he and Daniel Sturridge produced some lovely moments up front for the visiting side with Suarez seeing a free-kick clip off the United bar and fly over in the second half.
In the end, it counted for nothing for Brendan Rodgers's side with Javier Hernandez's opportunist finish 39 seconds into the second half enough to secure United a home tie with Norwich in the fourth round despite Liverpool's attacking play probably worthy of forcing matters to extra-time.
Hernandez's winning goal was a thing of real potency as the Mexican forward nudged Wayne Rooney's corner into the net with Jose Enrique failing to mark the forward in a crowded area.
United manager David Moyes will be relieved after making eight changes from the 4-1 thumping by Manchester City in the Premier League on Sunday.
PRE-MATCH - SUAREZ RETURNS FOR LIVERPOOL/NO VAN PERSIE: Robin van Persie misses out after he failed to recover from the groin injury that kept him out of Sunday's 4-1 Premier League defeat at Manchester City. Manager David Moyes makes eight changes with Javier Hernandez, Jonny Evans and Shinji Kagawa starting the match. Ryan Giggs is also in from the outset as United aim to rebuild morale after their thumping defeat by local rivals City. Patrice Evra, infamously racially abused by Suarez in 2011, was not in the United squad.
4' - UNITED PRESSURE: Nani finds Hernandez whose shot is blocked before Liverpool do well again moments later to block the effort from Nani on the rebound. Decent stuff from United.
10' - SUAREZ CLASS: Suarez to Enrique, but the chip to the back post is headed past his own post by Buttner with Sturridge lurking.
46' - HERNANDEZ GOAL: Hernandez flicks the Rooney corner into the net from close range. Awful defending by Liverpool. United lead 1-0.
64' - KAGAWA SHOT: Lovely driving run by Kagawa. Unloaded the shot from distance, but the ball clips the bar before flying over. Excellent play.
71' - SUAREZ EARNS SPACE: Ball breaks to Suarez in the United box. Earns himself some space with a neat turn, but he drives the ball into the side of the United net.
77' - ROONEY EFFORTS: Liverpool keeper Mignolet comes up with two quite magnificent stops to claw out powerful shots by Wayne Rooney. First from a free-kick then a thumping hit from distance.
87' - LAST LIVERPOOL CHANCES: De Gea across his line to claw out a Henderson effort. Suarez sets up Kolo Toure, but he drives the ball wide from 12 yards. Another chance eludes the visiting side.
3 - Javier Hernandez has scored in each of his last three starts for Manchester United.
4 - Liverpool's Lucas Leiva has now been booked in four of his last five appearances.
At Old Trafford, United have won each of their last six matches with Liverpool in all competitions.
TALKING POINT: Who will be the happier manager? Brendan Rodgers fielded a strong side, but could not penetrate the home side. United manager David Moyes made eight changes from the 4-1 loss at Manchester City. It was a risky ploy, but it paid off on the night for the home coach. Moyes will be happier after this one. Liverpool were wasteful in the second period.
MAN OF THE MATCH
Jonny Evans (Manchester United): Solid performance by the defender. Looked comfortable at the heart of the home defence alongside Chris Smalling.
Manchester United: De Gea 7, Rafael 7, Evans 8, Smalling 8, Buttner 7, Nani 7, Jones 7, Giggs 7, Kagawa 6, Rooney 7, Hernandez 7. Subs: Carrick 6, Welbeck 6, Januzaj 6
Liverpool: Mignolet 7, Toure 7, Sakho 7, Skrtel 6, Enrique 6, Henderson 6, Lucas 5, Gerrard 7, Moses 7, Suarez 8, Sturridge 7. Subs: Sterling 6, Kelly 7
THE MATCH IN A TWEET