Chelsea manager Pochettino hails 'priceless' Gallagher after Crystal Palace heroics
The England international scored twice after Chelsea had fallen behind to Jefferson Lerma's opener, before Enzo Fernandez's 94th-minute goal sealed the victory.
Gallagher, who has been linked with a move away from Stamford Bridge in the past two transfer windows, has missed only one of Chelsea's 24 league games this season when he was sidelined due to suspension.
He has made more than 30 appearances in all competitions and Pochettino said he was a player with "great commitment" to the team.
"Always trying to compensate every situation in an offensive and defensive situation and that is priceless to have a player like him," he told reporters.
"I'm so happy for him and I'm so happy for the team because it's a victory we needed, the three points."
Chelsea, who are 10th, had lost to Liverpool and Wolves in their last two league games.
Asked about Gallagher's future, the Argentine said: "What he told me was to stay at Chelsea. But then it's about him and the club.
"I'm not suffering with this type of thing, he still has one year more on his contract."
While pleased with the victory, Pochettino said Chelsea must avoid conceding early goals ahead of a run of tough fixtures including league matches against Manchester City and Tottenham, as well as the League Cup final against Liverpool.
"We need to be more consistent, we need to start the game in a different way...," Pochettino said.
"But yes, very pleased in the end because we needed the three points and now to prepare for the next week against Manchester City. That is going to be a good test for us before we prepare the final."