Fowler fired a 3-under-par 69, Points carded a 71 and McIlroy registered a 70 to finish the final round knotted at 14-under 274.
The playoff was held on the 18th hole at at Quail Hollow.
Points putted too hard on his birdie try, as did McIlroy, and each finished with pars. But Fowler, who had landed his second shot only 4 feet from the pin, holed his birdie attempt for the victory.
Webb Simpson (73) also could have joined the playoff but missed a 23-foot birdie putt on the final regulation hole, settling for fourth place at 13-under 275.
McIlroy's performance was enough to enable him to bypass Luke Donald for the world No. 1 mantle.
Astronomers offer more expansive view of universe
Attkisson leaves CBS News, reportedly over network's 'liberal bias'