Gerrard stroked home a second-half penalty while Luis Suarez added a double to take his league tally for the season to 22 from just 16 appearances.
Daniel Sturridge, back from injury, was also on target as Liverpool recorded their first league victory at Stoke in more than 29 years, and Gerrard was in no doubt of the importance of the result.
"It's big. Our record against Stoke in the league is poor away from home and we wanted to put that right today. I thought we showed tremendous character," Gerrard told Sky Sports.
"It's results like this we need if we want to finish in the top four."
The final scoreline by no means tells the whole story, with Liverpool guilty of squander a 2-0 lead.
Goals by Liverpool old boys Peter Crouch and Charlie Adam had the hosts level at the break, but the Reds went back in front through Gerrard's penalty before pulling away for the win.
"The first 40 minutes we controlled the game," Gerrard added. "It was very comfortable then we went a bit soft, made a couple of mistakes, and it became a real tough game from then on."
Gerrard was operating in a deep-lying position alongside Lucas in the Liverpool midfield and admitted he was still adjusting to his more withdrawn role.
"It's something we've been working on in the week and the manager's told me moving forward I'll play this role more," he said.
"It's going to take a little bit of time to get used to, but I've played it many times for England and a few times for Liverpool in the early days, so I'll be comfortable in there."