Holiday's baskets came back-to-back in the fourth quarter for the 76ers, who took a commanding 3-1 lead over the top-seeded Bulls in their best-of-seven Eastern Conference quarterfinal series.
Holiday finished with 20 points, eight rebounds and six assists while Spencer Hawes scored 22 to go with eight boards for the Sixers, who won despite hitting only 39.2 percent of their shots from the floor.
It was third straight triumph for Philadelphia since Bulls guard and reigning NBA MVP Derrick Rose went down with a season-ending knee injury in Game 1.
The Sixers will try to close out the series in Tuesday's Game 5 at Chicago.
Carlos Boozer led Chicago with a game-high 23 points and 11 rebounds.
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