Pole-sitter Franchitti, who led 161 of 225 laps, moved into a tie with Will Power atop the circuit's point standings with the victory. It was his third victory of the season and the 29th of his IndyCar career.
Helios Castroneves was ahead late in the race but was forced to pit for four new tires, allowing Franchitti to take the lead for good.
The Scotsman crossed the finish line 1.4 seconds ahead of Chip Ganassi Racing teammate Graham Rahal and ended the day with 271 points, tying Power with 10 races remaining in the year's 17-race schedule.
Oriol Servia came in third while Power, who started 17th, rebounded in the closing stages to finish fourth.
Danica Patrick came in fifth -- her first Top 5 IndyCar finish this season.