Gerrard made no mistake as he confidently dispatched it to David de Gea's right-hand corner.
Following the restart, Liverpool's pressing game had United on the back foot, and Lambert spurned a good chance when Gerrard played him in after robbing Ander Herrera of the ball around 30 yards from goal.
The Reds almost had a second minutes after the restart through Sterling after Coutinho had danced away from Herrera before feeding his teammate inside the box, but the teenager's effort deflected narrowly wide.
Rooney, who was given the captain's armband for the evening, levelled things up 10 minutes into the second half when he connected with Javier Hernandez's deep cross to send it back across Simon Mignolet's goal into the bottom corner.
United then had the lead almost immediately after when Mata's strike took a deflection to beat Mignolet before a bizarre incident had Rooney thinking he had his second of the evening.
Ashley Young's high cross hit the top of the net before rebounding back into play via the goal frame, and after Rooney tapped it home, the United players celebrated what they thought was their third.
However, the goal was eventually ruled out and a goal kick was awarded.
As Liverpool pressed for an equaliser, and incisive counter-attack saw Lingard arrive on the edge of the Reds' box late on to send a shot beyond Mignolet to wrap up the victory for Van Gaal's side.