Also in the East, Chicago squandered a 13-point lead in the final quarter to lose to Philadelphia while in the Western Conference, the Nuggets got back into their series against the LA Lakers with a 99-84 win in Denver.
Back from a one-game suspension for bumping into a referee, Rondo scored a triple-double with 17 points, 14 rebounds and 12 assists as the Celtics held off a spirited Hawks fightback to maintain control on their home court.
Forward Paul Pierce weighed in with 21 points and Kevin Garnett had 20 and 13 rebounds while guard Joe Johnson led the way for the Hawks with a game-high 29 points.
Rondo scored with a finger roll lay-up and then a hook shot to give Boston an early lead in overtime and Garnett's slam dunk gave them an 88-84 advantage with 28.1 seconds left.
Johnson and Tracy McGrady both missed three-point attempts for the Hawks as the Celtics held on to win.
"I felt good about all the shots I took," Rondo said after recording the seventh triple-double of his career in the postseason.
"My team mates told me to stay aggressive. Nights like tonight when I take a lot of shots, I finally found a way to get my team a win."
Boston, 40-38 ahead of the Hawks at halftime, appeared to break open a tight contest early in the final quarter with a 7-0 run.
Pierce poured in a three-point jump shot before Rondo added two more with a driving reverse layup to put the Celtics up 72-64.
When Garnett added two free throws and a two-point jumper, Boston were 76-65 ahead, the biggest lead of the night with six minutes left.
However, the Hawks clawed their way back and Johnson's three-pointer completed a 15-4 run to tie the game at 80-80 with 1:23 remaining.
Rondo missed a driving layup soon after and on the final play of regulation, with 3.9 seconds left, Pierce narrowly missed a jump shot after a clever feint.
Game Four is in Boston on Sunday.
In the high altitude of Denver, the Nuggets delivered a fast-paced exhibition of transition basketball to beat the Los Angeles Lakers 99-84 for their first win of the series to trail 1-2.
Guard Ty Lawson scored a game-high 25 points while JaVale McGee contributed 16 and Danilo Gallinari and Andre Miller 13 apiece.
Though All Star Kobe Bryant weighed in with 22 points for the Lakers, the visitors trailed by 24 points shortly before halftime and, despite briefly closing the deficit to four, they left themselves with too much ground to make up.
The Nuggets also host Game Four on Sunday.
Boston's Eastern Conference rivals Chicago again missed the injured Derrick Rose, squandering a 13-point lead in the final quarter to lose 79-74 to the Philadelphia 76ers.
Center Spencer Hawes scored 21 points and landed the go-ahead jump shot as the eighth-seeded 76ers ended the game with a rousing 23-5 run to take a 2-1 lead in the series.
Game Four is in Philadelphia on Sunday.