Six players scored in double figures for Boston. Rondo's double-double was his second straight and fifth overall since he returned from a knee injury on Jan. 17.
Jeff Teague had 26 points and DeMarre Carroll scored 24 off the bench for Atlanta, which lost for the 10th time in 11 games.
Back home after an 0-4 West Coast trip, the Celtics had only nine healthy players after a sore toe forced rookie Kelly Olynyk to the bench alongside regular starters Jared Sullinger and Avery Bradley.
The Hawks were missing five injured players, including starters Al Horford and Paul Millsap.
Kyle Korver had 17 points for the Hawks, including four 3-pointers.
Celtics coach Brad Stevens decided to start Bayless alongside Rondo and have Gerald Wallace (12 points) come off the bench. Bayless had his best game since being traded to the Celtics on Jan. 6, with 21 second-half points - including four 3s in the third quarter.
The Hawks hit their first six shots en route to a 13-2 lead just 3:25 into the game, then raced off to a 23-8 advantage before the Celtics rallied behind Rondo's 11 first-quarter points to close to 27-25.
Boston took a 58-56 halftime lead. Carroll had 17 points for the Hawks, who hit six 3s in the first half - three by Korver - to keep it close.
Teague scored 10 points in the third quarter, and Boston took an 81-79 lead into the final period.
Boston entered the game with the fourth-worst record in the NBA. The Hawks, even with their recent woes, still own the eighth and final playoff spot in the Eastern Conference.
-- NOTES: Korver extended his NBA-record streak to 126 games with at least one 3-pointer. ... Olympic giant slalom gold medalist Ted Ligety was in attendance.
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