Yohan Cabaye sealed the victory with an 89th-minute penalty after Chris Brunt tripped man-of-the-match Wilfried Zaha just inside the box.
Bolasie last scored at Selhurst Park on New Year's Day in January 2013 and ended his long drought when he powerfully headed home a Cabaye cross to give Palace a well-deserved lead after 68 minutes.
West Brom, managed by former Palace boss Tony Pulis, had not conceded a goal or lost away in the league going into the match and for long periods they seemed content to soak up the home team's pressure and rarely posed the Palace defence any problems.
Palace moved on to 15 points and into third place in the table, at least until Saturday's later matches which include second-placed Manchester City playing Newcastle United and West Ham United, who were third at the start of the day, playing at Sunderland.
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West Brom remain on eight points in 15th spot.
(Reporting by Mike Collett; editing by Toby Davis)
