Overnight leader, Kevin Stadler collapsed to a 76 on a wet and windy final day yesterday.
Kapur rounded off a modest week with a one-under 70. Kapur, the lone Indian to make the cut this week, ended the tournament at four-over 288. Jeev Milkha Singh and Gaganjeet Bhullar had earlier missed the cut.
Kapur opened with a bogey on first but birdies on fifth, seventh, 10th and 11th saw him climb to three-under, but he once again had problems on the back nine at the Le Golf National as he dropped three bogeys between 13th and 16th. A closing birdie on 18th did give him a positive feel unlike the second and third days when he bogeyed the 18th.
But the former US Open Champion still needed Stadler to miss from two feet for par on the 18th, an effort which would have forced a sudden death play-off.
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With McDowell then dropping his only shot of the day on the 18th after finding heavy rough off the tee, Stadler needed to par the 18th to force a play-off but missed from two feet just as McDowell left the recording area to prepare for extra holes.
"I'm very surprised," McDowell said after claiming his tenth European Tour title. "Midway through my second glass of red wine last night, when I was very disappointed with my back-nine performance on Saturday, I really didn't think I'd be a) standing here with an opportunity to be in a play-off and b) with a trophy in my hands."
Stadler found himself five clear of the field when playing partner Jaidee got off to a terrible start and local favourite Victor Riu followed a birdie on the first with a double bogey on the second after hitting his tee shot in the water.