Gallagher came off the bench to score his first goals since a summer move from Blackburn and lift Leicester to within three points of the Championship summit.
He opened the scoring with a rebound from a Matty Fryatt penalty before clipping in a delightful second from 30 yards.
Both sides had been dire in the first period and Pearson admitted that having the likes of Gallagher, DJ Campbell and Martyn Waghorn available on the bench was the difference between the sides.
He said: "We have players who can bring quality to the team when they are not involved and that certainly proved the case.
"All the subs had positive impacts.
"I'm pleased for Paul as he has had to be patient since he's been here. He's playing slightly out of position and has done very well for us.
"In the time he was on he had four or five efforts on target and the second one was a great strike.
"We fell into the trap of playing in a similar way to them in the first half, we were too direct. But after the break we were much more varied and passed the ball better and were worthwhile winners in the end."
Crystal Palace boss Neil Warnock was unhappy with referee Roger East for allowing Gallagher's opener.
East awarded the penalty when Nick Carle tripped Gallagher but Warnock felt the Scot was inside the area when Fryatt took his spot-kick.
He said: "It was a Sunday league tackle for the penalty but the lad who scored the goal was three yards inside the box when it was taken.
"Rules are rules. We've heard all week about a beach ball and
then they allow a goal like that.
"He brushed past the referee on his way into the area so he can't say he hasn't seen it.
"We came with a positive attitude but we lack quality up front. We haven't got the players to excite anyone in attack."
Warnock has been linked with a dramatic return toLeague Two club Notts County - whom he steered to promotion to the top flight back in 1991.
He remained in humorous form when asked about the chances of a return to Meadow Lane however and insisted his focus was on city rivals Nottingham Forest, whom his side host on Saturday.
He said: "The Notts County job for £2.5million a year? I'm not interested, obviously.
"We have got Forest to worry about now. They've just won five in a row so that will be another very tough game."