Baddeley chipped to 8 feet on the fourth extra hole -- the 18th -- and made the putt. Chopra, who made several clutch putts in regulation and in the playoff, dragged his par putt wide from a slightly shorter distance, giving the Australian the win.
It was the fifth time in six years that the Masters was decided in a playoff. The 18th played as one of the most difficult Sunday because of the wind, with only four birdies there in the final round.
'I felt I could eventually wear him down,' Baddeley said. 'I was hitting the ball really well.'
Baddeley missed an 8-foot birdie putt on the first extra hole after Chopra missed his from twice that distance. Both missed long birdie putts on the second extra hole.
On the third extra hole, Chopra made a difficult 10-foot putt for par after Baddeley was left with a tap-in.
Baddeley closed with a 2-under 70 to match Chopra (71) at 13-under 275 on the Huntingdale course. Chopra birdied Nos. 15 and 16 in regulation, while Baddeley pulled into a tie for the lead with a birdie on 17.
Australia's Stuart Appleby made a double bogey on the 18th for a 69 that left him two strokes back in third. After his tee shot went into a fairway bunker, he pulled his 8-iron from the sand into the corporate marquee area.
His shot from the drop zone finished 25 feet from the hole, and the long uphill putt for par went 6 feet past. He two-putted from there for a 6.
Australia's Robert Allenby, the leader after each of the first two rounds, closed with a 73 to tie for 10th at 7 under. Rory McIlroy, the 18-year-old from Northern Ireland, was another stroke back after a 73.