The American produced an impressive back-nine surge, which included five birdies, at Ridgewood Country Club to ensure victory at the play-offs opener.
Mahan later spoke of securing a Ryder Cup spot for Gleneagles in September and the 32-year-old's 23-place rise up the rankings will further bolster his confidence.
South Africa's Charl Schwartzel dropped out of world's top 20 while Wales' Jamie Donaldson moved up to 27th after victory at the weekend.
Donaldson ensured himself of a place in Paul McGinley's European team for the Ryder Cup after winning the Czech Masters by two shots in Prague.
Rory McIlroy remains at the summit with the top six positions unchanged.
Jason Day moved from ninth to seventh after the Australian finished tied second at the Barclays alongside Stuart Appleby and Cameron Tringale, who move up by 97 and 43 places respectively.
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