The 27-year-old finished into an open goal to make it 2-0 as he converted a rebound after Eagles goalkeeper Vicente Guaita had parried Raphinha’s shot.
Earlier on, Leeds had taken a third-minute lead when Jack Harrison’s strike from the edge of the penalty area took a big deflection off Gary Cahill and looped past Guaita.
Bamford’s century of goals includes 21 on loan at MK Dons, eight on loan with Derby, 33 with Middlesbrough and 38 with his current side.
The most important thing is getting the three points but it is nice to get to 100 career goals It is probably long overdue but nice to get there.”
Bamford who was with Chelsea for five years but had seven loan spells elsewhere and never played a competitive game for the Blues.
The victory moves Leeds up from 11th and above Arsenal to 10th, while Palace, who themselves would have gone into the top half with a win, remain 13th.
Bamford’s 12th Premier League goal of the season means only two English players – Tottenham’s Harry Kane and Everton’s Dominic Calvert-Lewin, both with 13 – have scored more goals than him.