Not for the first time, Liverpool could be grateful to Steven Gerrard for his nerveless precision from the spot. The captain scored his 10th and 11th penalties of the season in all competitions as his club maintained their Premier League title challenge and made light of a remarkable refereeing blunder into the bargain.

One of the principal talking points of a dramatic afternoon came at the end of the first half when Andy Carroll, West Ham's former Liverpool striker, who was on a mission to prove and score points against his old side, clouted the visiting goalkeeper, Simon Mignolet, following Mark Noble's corner. Guy Demel duly flicked home his first goal in West Ham colours but the linesman, Stuart Burt, was flagging. The goal looked set to be disallowed. Yet, after a lengthy conversation with Burt, the referee, Anthony Taylor, overruled him. West Ham were level. Taylor happens to hail from Manchester; cue Liverpudlian conspiracies.

Gerrard, however, cut through them when he blasted in the second penalty and it was West Ham that were left to spit the feathers over the other big discussion point even if, on balance, Liverpool were value for the victory. Despite a disciplined performance, West Ham did not do enough in the final third.

The home side's manager Sam Allardyce and everybody with West Ham in their hearts – or, indeed, Chelsea and Manchester City – could not believe that Taylor chose to penalise Adrián, the West Ham goalkeeper, for bringing down Jon Flanagan, after the Liverpool full-back had nicked the ball in front of him inside the area. It was a close call and Brendan Rodgers, the Liverpool manager, admitted that it was one of those which tended to feel a "wee bit contentious" when they went against you. Rodgers also suggested that Taylor was "chasing the game" after the controversy of the West Ham equaliser. Adrián did make contact with the ball as the players initially came together but, as Flanagan continued to try to reach it, the goalkeeper grabbed at his foot.

The arguments raged at the time and long into the night while there were boos from the Upton Park crowd at the final whistle. Allardyce's anger was fuelled, in part, by the fact that a committed performance had yielded nothing; West Ham did carry the fight to Liverpool, particularly in the first half. But Allardyce appeared to undermine his arguments about injustice when he agreed that Demel's equaliser ought not to have stood. He seemed more preoccupied with simply complaining about the officials.

This was not a vintage performance from Liverpool, even if they looked better after Rodgers switched from 4-3-3 to a diamond midfield at half-time. They only cut loose in an attacking sense after Gerrard's second penalty but it was nevertheless a ninth consecutive league victory and the excitement around the club, as they eye a first championship since 1990, is palpable.

The visit of City to Anfield next Sunday has all the hallmarks of a title decider and it was interesting to hear Rodgers lay the psychological groundwork, when he talked of the money that City had spent in order to win the league and the Champions League. But his team, as he acknowledged, is playing without any inhibitions.

This was a gutsy win, in which West Ham's physical power had to be contained, and it came not only from Carroll but Mohamed Diamé, who drove inside from the flank, and the central defenders, Winston Reid and James Tomkins. Carroll's duel with Martin Skrtel was box-office stuff.

Liverpool were content to punch on the counter, to harness the pace and quicksilver quality in their ranks and they flickered, mainly through Luis Suárez. The opening goal came on the break, following a direct ball from Gerrard and Suárez was central to it. Tomkins had played him well up to that point, even if the Uruguayan had managed to wriggle clear of the West Ham defence to bend a 20th-minute shot against the crossbar, but the home team did not escape when he darted on to Gerrard's pass and touched inside Tomkins. The defender left his hand out, the ball struck it and it was an obvious award.

Up stepped Gerrard and up flashed the Sky TV graphic on both of the stadium's big screens about where the Liverpool captain had placed his most recent penalties, which was weird, even if Adrián surely had to be pre-armed with that kind of information. Gerrard still sent him the wrong way, planting the kick low into the bottom right-hand corner.

West Ham fought back. Literally. It felt inconceivable that Taylor could not see Carroll leading with his arm to clump Mignolet on the head but Demel's goal would stand. Carroll almost got the goal he craved on 61 minutes only for his header from Diamé's cross to thump against the crossbar and the game turned again on the second penalty, which Gerrard hammered into the other corner.

Liverpool might have embellished the final scoreline. Suárez hit the crossbar again with an impudent chip while he was also denied one-on-one by Adrián and the goalkeeper saved smartly from Raheem Sterling. Liverpool roll on.