Deadline-day signings Scott Dann, Joe Ledley and Tom Ince were included in the team and two of the new boys made an instant impact against lacklustre West Brom with Ince and Ledley grabbing first-half goals.
West Brom introduced Thievy Bifouma at the start of the second half and the on-loan Espanyol striker scored 40 seconds into his debut.
"Tom took his goal with aplomb and he did all the unglamorous stuff. We are pleased with him, Dann and Ledley," said Pulis who has never been relegated in his 21 years as a manager.
"I am pleased for the group, it is the group that has taken us to where we are at the moment and it will be the group that decide whether we're good enough to stay in the Premier League," he told reporters.
Palace, who were favourites for relegation at the start of the season, have been rejuvenated since Pulis replaced Ian Holloway.
The Londoners have won six games since the Welshman took charge in November to climb to 13th in the table, three points clear of the drop zone.
"We've got a very tough run of games coming up. The important thing is that you stay focused," said former Stoke City boss Pulis.
"I've managed in the Premier League for six years now and the one thing you should never do for a club our size is get complacent.
"It is important you keep picking points up. The great thing about today is we've got a win and three points in the Premier League is enormous."
West Brom are third from bottom on 23 points, having won once in 15 matches.
"We have 13 cup finals and 13 battles to go," said Spanish manager Pepe Mel who has gone four games without a victory since taking over from the sacked Steve Clarke.
"We must win as many of these as we can and the players must come with me for this battle."