Tampa Bay kicker Patrick Murray was wide right on a 54-yard field-goal attempt as time expired.
The Bucs (4-10), who entered the game without three injured defensive starters, had six more players ruled out after getting hurt Monday night.
Falcons running back Devonta Freeman (22 carries, 126 yards) provided a 24-14 margin with a 32-yard touchdown run on third-and-2 with 7:58 remaining. The Bucs answered on Jameis Winston's 16-yard pass to Adam Humphries with 4:07 to play.
From there, Tampa Bay eventually regained possession when Bucs defensive tackle Clinton McDonald dumped quarterback Matt Ryan for a 3-yard sack on third-and-9 just past the two-minute warning.
Winston completed three passes on Tampa Bay's final drive, driving the Bucs from their 29-yard line to Atlanta's 36, setting up Murray's unsuccessful attempt to force overtime.
Winston completed 27 of 35 passes for 299 yards and three touchdowns in his most efficient effort of the season. Ryan was 17 of 31 for 212 yards and one score.
In the third quarter, the Bucs pulled within 17-14 on Winston's 42-yard pass to Mike Evans, who outfought two defenders in the end zone. Tampa Bay preserved that three-point deficit when Will Gholston blocked Matt Bryant's 33-yard field-goal attempt.
The Falcons led 17-7 at halftime, pulling away with a 10-point second quarter.
Atlanta gained its advantage when Freeman lost a fumble at the 1-yard line, but tight end Levine Toilolo recovered in the end zone for a touchdown.
The Bucs tried to answer back, but Peyton Barber lost a fumble at Atlanta's 5-yard line and Falcons defensive tackle Dontari Poe recovered.
The Falcons tacked on a 57-yard field goal by Bryant with 3:12 remaining in the half for a 17-7 lead.
Atlanta opened the scoring with Ryan's 6-yard pass to Justin Hardy.
On the ensuing drive, Tampa Bay pulled into a 7-7 tie with Winston's 30-yard scoring pass to rookie tight end O.J. Howard, who sustained a game-ending ankle injury on the play.
NOTES: The Bucs played without DT Gerald McCoy (biceps), LB Lavonte David (hamstring) and CB Vernon Hargreaves (hamstring). Hargreaves missed his fifth straight game. Also inactive for Tampa Bay was RB Doug Martin, the team's leading rusher, for what was termed violation of team rules. ... The Falcons were without RB Tevin Coleman (concussion) and G Andy Levitre (triceps). ... Bucs TE Cameron Brate (knee) left in the first quarter and OL J.R. Sweezy (ankle) departed in the second quarter. ... Former Bucs coach Jon Gruden (2002-08), who won Super Bowl XXXVII, was inducted into the franchise's Ring of Honor at halftime. Gruden worked the ESPN "Monday Night Football" broadcast of the Monday game. ... Falcons players wore a No. 60 decal on the back of their helmets to honor linebacker Tommy Nobis, the initial first-round pick of the Atlanta franchise in 1966. Nobis died on Dec. 12.