The only goal of the game was scored late in the first half as Daniel Sturridge opened his account for the campaign with a low drive that found the bottom corner.
However, there was late drama when debutant Simon Mignolet made himself an instant hero among the Merseyside faithful by saving Jonathan Walters's penalty.
Here, Sports Mole takes a closer look at the action.
On target 11
On target 4
Was the result fair?
Despite the narrow margin between the teams, Liverpool were fully deserving of the three points. Brendan Rodgers's side took control of the game early and always looked to push forward. In contrast, Stoke appeared short of ideas, and although they came withing a whisker of earning a draw, it would have been an unfair result on the hosts.
It did not always run smoothly for the Merseysiders, but they mixed dynamism going forward with solidity at the back to get the win. As expected, most of their creativity came from midfield, with Philippe Coutinho and Steven Gerrard pulling most of the strings. These sort of fixtures have seen the Reds fail to come through with a victory time and again in the past, so they will be delighted that their season has started positively.
A new era for the Potters was marked with a lack of identity at Anfield as they looked bereft of ideas going forward. As is likely to be a recurring theme this season, the defence earned their corn thanks to the kind of dogged display that they have made their own in recent years. Their standout performer was goalkeeper Asmir Begovic, who pulled off a string of remarkable saves to give his team a fighting chance of earning a point. There would have been no complaints from Stoke if Walters's penalty had found the net late on, but it would have been a very fortuitous point indeed.
Sports Mole's man of the match
Daniel Sturridge: While Asmir Begovic put in a mammoth display for the away side, it was Sturridge who was the real difference between the teams. The striker was sharp as a button from the first whistle, causing the Stoke defence innumerable problems with his pace and clever positioning. He was rewarded with a goal of clinical quality - firing the ball sweetly into the bottom corner from the edge of the penalty area. He was just as busy in the second half and could easily have bagged himself a couple of more goals.
Daniel Agger's handball to gift Stoke a late penalty was nearly very costly for Liverpool. Quite what he was thinking is unclear, but he owes Mignolet big time for saving Walters's spot kick.
With the wet conditions, Martin Atkinson could easily have stopped play consistently due to wayward challenges from the players. However, the official allowed the game to flow as much as possible. There were one or two confrontations late on, but he dealt with those in a measured manner.
Liverpool: The Reds continue their Premier League campaign next Saturday when they make the trip to Aston Villa.
Stoke: It is back to the drawing board for the Potters as they welcome Crystal Palace to the Britannia Stadium.