The lone goal came from Daniel Sturridge about midway through the first half, but there were plenty of positives for the home side.
Iago Aspas, Kolo Toure and Simon Mignolet all debuted for the Reds, and each player had a decent game.
On this performance, Reds fans will hope their side can continue to navigate the period without Luis Suarez and improve even more when the Uruguayan returns—if he stays.
Here are the ratings for each Liverpool player.
Simon Mignolet - 7
The Belgian goalkeeper didn't concede a goal, but came close to inflicting harm on the side with a big mistake in the first half. He flapped at a cross while challenging Peter Crouch in the first half, and was lucky that Robert Huth could only connect with the crossbar. He was otherwise very steady, and his late penalty save, and the save of the follow-up, increases his score greatly.
Glen Johnson - 6.5
Glen Johnson was a steady presence overall, he provided an outlet for his side when attacking and was quite solid defensively.
Kolo Toure - 6.5
Kolo Toure was a bit of a threat on set-pieces, almost opening the scoring for the side when he rocked the crossbar from a header following Steven Gerrard's corner. He wasn't the Kolo Toure of old, but proved a much better partner for Daniel Agger while dealing with Stoke City's threats.
Daniel Agger - 6.5
Like Mignolet, Daniel Agger's part in the penalty had an effect on his final score. The Danish defender continued his good form from last season, snuffing out the majority of Stoke City attacks, keeping Crouch under wraps in the process.
Jose Enrique: 6.5
Part of a steady back line, Jose Enrique was unlucky not to get on the scoresheet in the first half after being sent through by Philippe Coutinho. He was solid defensively and linked well with his wide partner in the attacking third.
Steven Gerrard: 7.5
Steven Gerrard was great in his deeper-lying role, pinging balls across the pitch and dictating proceedings for his side. His set-piece delivery was impeccable.
Lucas Leiva: 7
Lucas Leiva did what he's positioned in midfield to do, snuffing out Stoke City's threats in the middle and covering for the full-backs when they attacked.
Jordan Henderson: 6.5
Jordan Henderson was hard-working as always, but missed two good opportunities for his side. He was unlucky to hit the post the second time around though. It was an okay outing from the youngster, but he still has a long way to go.
Iago Aspas: 7
All Iago Aspas needed to cap off a solid debut was a goal. He was good in possession, worked efficiently and linked with his teammates well.
Daniel Sturridge: 7.5
Daniel Sturridge's fantastic long-range strike gave Liverpool the lead, proving to be the eventual winner. He proved troublesome for Stoke's back line, trying to create opportunities for his teammates and himself.
Philippe Coutinho: 8
Philippe Coutinho was instrumental in the attacking third, playing some nice slide-rule passes to his teammates in tight areas. Most, if not all, of Liverpool's best attacking moves came when the young Brazilian was involved, and that's a testament to his impact.
Raheem Sterling: 6
Did what was needed to keep Stoke City's defense honest with his pace, skill and link-up with his teammates. Worked well defensively also.