Heat 88 Bulls 65
Miami held hosts Chicago to 25 percent shooting to take a 3-1 lead in the Eastern Conference semi-final series.
LeBron James had 27 points and eight assists, while Chris Bosh added 14 points, as the Heat held the Bulls to their lowest scoring output in franchise playoff history.
Tope seed and defending NBA champions Miami can clinch the best-of-seven series at home in Wednesday's Game Five.
Carlos Boozer had 14 points and 12 rebounds, Jimmy Butler scored 12 points but Nate Robinson missed all 12 of his field-goal attempts and did not score in 32 minutes.
The Bulls had 33 first-half points and followed that with a franchise playoff-record low nine in the third quarter and trailed 61-42 after Norris Cole swished a three-pointer at the buzzer.
Miami's lead stretched to as many as 26 points in the final stanza.
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Grizzlies 103 Thunder 97 (OT)
Mike Conley had 24 points and four steals as hosts Memphis overcame a 17-point deficit to stun Oklahoma City and take a 3-1 lead in the best-of-seven Western Conference series.
Zach Randolph had 23 points and 12 rebounds and Marc Gasol added 23 points, 11 rebounds and six blocked shots for the Grizzlies, who outscored the Thunder 9-3 in the extra session.
Memphis can clinch the series with a Game Five victory in Oklahoma City on Wednesday.
Kevin Durant scored 27 points, Kevin Martin tallied 18 points and Serge Ibaka had 17 points and 14 rebounds for Oklahoma City, which led 46-29 with 4:26 left in the second quarter before Memphis rallied to tie the score at 72-72 with 1:46 left in the third quarter.
Tony Allen and Randolph opened overtime with baskets before Derek Fisher hit a three-pointer with 1:54 to play for Oklahoma City's lone points of the session.
Gasol hit a key basket with 22.8 seconds left to make it 100-97, and Gasol (one) and Tayshaun Prince (two) combined for three free throws as the Grizzlies beat the Thunder for the third straight game.
Randolph and Gasol each hit one of two free throws in the final minute of regulation to give Memphis a 94-92 lead.
Durant tied the game with a driving scoop shot with 6.4 seconds remaining and Randolph had his last-second shot attempt swatted away by Kendrick Perkins.