Liverpool bounced back from their midweek Carling Cup humbling by beating West Ham with goals from Xabi Alonso and Boudewijn Zenden.
Alonso's curling shot went in via a slight deflection off Tomas Repka after the Hammers failed to clear a corner.
The home side should have added to their tally but Sami Hyypia's shot was cleared off the line while Fernando Morientes had a free header saved.
But Zenden wrapped up the win with an angled shot which went in off the post.
Liverpool made an uncertain start despite the return of several leading players in the wake of their shock loss to Crystal Palace on Tuesday.
Djibril Cisse and Garcia each failed to convert early chances for the Reds, with both players guilty of going for goal when passing to a team-mate seemed the better option.
Reds keeper Jose Reina's poor kicking gave a hint of home nerves while the Hammers always posed a threat as their young side attacked in numbers and with pace.
Alonso eventually eased the home crowd's worries when he seized on a poor Nigel Reo-Coker clearance from a Garcia corner.
Liverpool began to gain a stranglehold of the game but had to remain wary of the visitors, who threatened when Marlon Harewood's clever flick at the near post went over.
The Reds quickly built up a head of steam after the interval and were only denied a second goal when Paul Konchesky cleared Hyypia's shot off the line after another corner was not properly cleared.
Reina almost let a low Repka cross squeeze through his grasp but West Ham's threat was dwindling.
The struggling Morientes then had an excellent chance to extend Liverpool's lead only to head straight at keeper Shaka Hislop from six yards.
Garcia also had a shot saved as well as glancing a header wide as Liverpool failed to turn their chances into goals.
But substitute Zenden eased any home fears by grabbing his first goal for the club.
Liverpool manager Rafael Benitez:
"I had confidence in the team. The team work hard in training and you could see an organised team trying to win until the end.
"The team is stronger but you need to win and then people will believe."
Benitez played down the fact that his strikers failed to score and said: "If you have the midfielders going forward and scoring goals I will be happy."
West Ham boss Alan Pardew:
"It's like two boxers - if one's a champion you have to bloody his nose.
"We didn't really do that. We were okay for a little while but they had control of the game.
"This is a big jump we are taking and that was underlined."
Liverpool: Reina, Finnan, Hyypia, Carragher, Riise, Luis Garcia, Gerrard, Alonso, Sissoko, Cisse (Zenden 73), Morientes (Crouch 90).
Subs Not Used: Hamann, Carson, Warnock.
Booked: Morientes, Finnan.
Goals: Alonso 18, Zenden 82.
West Ham: Hislop, Repka (Collins 81), Ferdinand, Gabbidon, Konchesky, Benayoun, Reo-Coker, Mullins, Etherington (Sheringham 67), Bellion (Aliadiere 60), Harewood.
Subs Not Used: Bywater, Dailly.
Ref: U Rennie (S Yorkshire).