The Celtics took a 2-1 lead in the opening-round playoff series and will host Game 4 Sunday.
Rondo added 14 rebounds and 12 assists in his first game back after serving a one-game suspension for making contact with an official in the opening game of the series.
Joe Johnson hit a 3-pointer for Atlanta to tie the score with 1:24 to go in the fourth period and neither side could score again in regulation.
Rondo produced Boston's first four points of the extra period and the Celtics did not trail throughout the overtime.
Paul Pierce scored 21 points for Boston while Kevin Garnett had 20 points and 13 rebounds. The Celtics made 10 more free throws than did the Hawks and limited Atlanta to 37 percent shooting from the field.
The teams combined to go just 8-of-33 from 3-point range.
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