While the AFC North leading Ravens improved to 9-2 with their fourth straight victory, Philip Rivers and the Chargers slipped to 4-7, having never trailed Baltimore in regulation on a sunny afternoon at Qualcomm Stadium.
A touchdown by wide receiver Malcom Floyd early in the second quarter put San Diego in control for much of the game but Baltimore forced overtime with a late score by tight end Dennis Pitta and a Tucker field goal with just three seconds left.
Both sides had two plays apiece in extra time but it was the Ravens who prevailed as Tucker coolly powered the ball through the uprights to end a 12-play drive.
Baltimore quarterback Joe Flacco completed 30 of 51 passes for 355 yards and one touchdown while Rivers threw for 228 yards and one touchdown as his demoralised team suffered a third straight loss.
Both teams struggled on offense during a scoreless first quarter before the Chargers went ahead when Rivers connected with Floyd for a 21-yard touchdown to cap a nine-play drive.
A 47-yard field goal by Nick Novak gave San Diego a 10-0 lead with just over three minutes left in the second quarter, and helped by swarming defense the Chargers maintained that advantage by half-time.
Baltimore put their first points on the board early in the third quarter when Tucker ended a seven-play drive with a 43-yard field goal.
Though the Ravens kept pressing, the Chargers held firm with water-tight defense and survived an 11-play drive by Baltimore to remain 10-3 up going into the final quarter.
San Diego continued to batter away at the much vaunted Ravens defense, beginning the fourth quarter with a well-orchestrated 13-play drive that ended in a 30-yard field goal by Novak to put them 13-3 up.
The Ravens finally found a way to the end zone after Chargers nose tackle Antonio Garay was penalised five yards for a neutral zone infraction, Flacco hitting Pitta for a four-yard touchdown with just over four minutes left.
Baltimore continued to attack and, with just three seconds remaining, they tied the score at 13-13 when Tucker ended a 12-play drive with a 38-yard field goal to force overtime.