Gerrard converted from the spot in each half before missing a third penalty after Nemanja Vidic was sent off before Luis Suarez scored a late third to keep Liverpool, who have a game in hand on Chelsea, firmly in the title hunt.
Though chances were scarce during the first half, Liverpool played with a far greater intensity and tempo, and took the lead on 34 minutes.
Rafael was fortunate not to be shown a second yellow card in as many minutes after handling the ball following Suarez's clever touch and Gerrard sent David de Gea the wrong way from the penalty spot.
United briefly woke from their slumber as Wayne Rooney tested Simon Mignolet just before half-time, but Liverpool were awarded another penalty in the opening minute of the second half.
Phil Jones was penalised for a nudge on Joe Allen and, though De Gea guessed correctly on this occasion, Gerrard's precise penalty was beyond the United keeper's reach.
The Red Devils saw two penalty appeals waved away in the ensuing 10 minutes before Liverpool were awarded a third spot-kick when Daniel Sturridge went down under Vidic's challenge which resulted in a second yellow card for the United captain.
Gerrard stepped up for his hat-trick, only to strike the post, while Liverpool could have had a fourth penalty moments later when Sturridge appeared to be tripped by Michael Carrick.
Suarez was thwarted by a brilliant save by De Gea before the Uruguayan did beat the United keeper on 84 minutes with a neat finish after controlling Sturridge's mis-hit shot.
The manner of the defeat against their arch-rivals will be even more galling for United, who now have to lift themselves for the second leg of their UEFA Champions League tie at home to Olympiakos on Wednesday.
This time last year United were 29 points ahead of Liverpool. They are now 14 behind their bitter rivals with nine matches of the season left and the 11-point gap to fourth place looks insurmountable.
United were given an early warning sign after just two minutes when Sturridge sprinted past Vidic but shot wide.
Suarez then latched onto Jon Flanagan's cutting pass and sprinted into the United box but he did not go down when Marouane Fellaini pulled his shorts.
Sturridge again got the better of Vidic and Jones with a burst of pace, but he fluffed his shot, and De Gea made his first save from Allen.
Flanagan was booked for his third foul of the game and Rafael soon joined him for a pointless sliding tackle on Gerrard.
Moments later and Rafael handed the Reds the lead when the ball struck the Brazilian's outstretched right hand as Suarez tried to guide the ball past him.
Gerrard made no mistake from the spot, tucking the ball inside De Gea's left-hand post.
United had a strong five-minute spell before the break which involved Rooney drawing a top save from Mignolet, but just 30 seconds after the restart they imploded.
Jones clattered into the back of Allen and the referee pointed to the spot and Gerrard placed the ball to De Gea's left again.
United thought they should have had two penalties for a handball by Glen Johnson and a foul on Rooney by Martin Skrtel but referee Mark Clattenburg disagreed.
Robin van Persie, the man who won United the title last year, glanced a free header feebly wide from six yards.
A nightmare afternoon plumbed new depths when Vidic was given a second yellow card for bringing down Sturridge, although replays suggested the England striker had dived.
The only crumb of comfort for United was that Gerrard missed his hat-trick opportunity by hitting De Gea's right-hand post.
De Gea saved well from Suarez with eight minutes left but the Uruguayan did not miss moments later to complete a miserable day for United.