The 34-year-old twice stepped up to beat Adrian from the penalty spot as Liverpool recorded its ninth consecutive victory and returned to the top of the table.
Gerrard sent Adrian the wrong way from 12 yards on 44 minutes after Luis Suarez's deft flick struck the arm of James Tomkins and powered in his second on 71 minutes after the goalkeeper felled Jon Flanagan.
The win returns Liverpool to the Premier League summit ahead of next Sunday's title showdown with Manchester City, and after the match Rodgers paid tribute to his captain.
"I thought he was outstanding today, his range of passing, his pass for the first goal and his coolness," Rodgers told reporters.
"It's not by accident," Rodgers said of his captain's penalty success. "He studies the goalkeepers, he analyzes the pattern of a goalkeeper’s dive, where they make saves. He’s got great variety, he can put the ball anywhere and as a manager to have someone as cool and as calm as him in those pressure situations, he did fantastically well.
"We had to change the game at halftime. We were in a 4-3-3 – I’m always trying to get the two front boys in the team, but I didn’t think it was quite working for us. We couldn’t dominate the game as much as we’d like we went to a diamond in the second half and put the strikers closer together to try which could stretch them a bit more. I thought we were dominant in the second half and Steven was pivotal in that for us."
Sam Allardyce, meanwhile, was critical of referee Anthony Taylor and his assistants after a match which saw two penalties awarded and a controversial Guy Demel goal allowed.
"We want to play a game of football and we want the team that wins to win through the way they've played, not through what decision the referee might or might not have got wrong," Allardyce said. "There are two decisions - one for Liverpool and one for us - that leads to controversy and frustration due to the management of the players by officials who weren't quite at the level we expect.
"We gave all we could give and tried our best to upset Liverpool's winning streak, but unfortunately for us they've won on two penalties rather than their attractive football."