Those mistakes allowed Kang to use a 71 in a testing breeze at the Golf Club of Houston to finish the day on 17-under-par 199 with one round left as he targets a last-minute berth at the U.S. Masters.
Fowler (67) was on 14-under, with fellow American Russell Henley (69) another shot back.
Kang needs to win on Sunday to qualify for next week's Masters, the first major of the year, and if he does he might like to thank Fowler's putter.
"I'll just stick to my game plan," Kang told PGATour.com, aware of the Sunday forecast for strong storms that could make for a long day.
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"It was very hard work (today). Greens got firmer, faster. I tried to really grind it out today and I did pretty good."
Kang heard the cheering and clapping from the preceding group following the popular Fowler, who delighted his overflowing gallery by picking up eight birdies in the first 14 holes, including a monster 50-footer putt at the seventh hole.
His first dropped shot did not come until the par-four 17th, where he missed a five-footer, a minor hiccup compared to the final green, where his first putt from 55 feet stopped more than four feet short of the hole.
Fowler had a look of disbelief when he missed the second putt, and his expression turned ashen after his next miss from inside four feet.
"Can't really dwell on the last two holes," Fowler said. "I was trying to avoid a spike mark on 17 and my second putt for par on 18 was supposed to go right and it moved left on me.
"It's unfortunate but we've put ourself in position to win so ... can't really dwell on the last two holes."
Kang had no such problems on the final green, sinking a testing four-footer to put himself in prime position to earn his first PGA Tour victory at the age of 29.
(Reporting by Andrew Both in Cary, North Carolina, editing by Gene Cherry/Greg Stutchbury)
