Logano and Kevin Harvick both breezed past Mark Martin with just over three laps to go in the 400-mile, 200-lap race. Martin had been trying to stretch fuel, but when he faltered, Logano was able to hold off Harvick.
Logano entered the weekend in 16th place in the points standings. After winning the pole Friday, he took Sunday's race by one second over Harvick, who is safely near the top of the standings.
There are three races left before the Chase.
Points leader Jimmie Johnson lasted less than 60 laps before engine trouble knocked him out.
It was the third Cup win of Logano's career, and it came after he posted the ninth-fastest pole-winning speed in NASCAR history during Friday's qualifying.
Johnson, Kyle Busch and Dale Earnhardt Jr. were among the big names to have problems, but the race was a clean one for Logano in his No. 22 Ford. He was battling Kurt Busch for the lead at the very start and needed only to outlast Harvick at the end.
Kurt Busch did finish third, improving his chances of reaching the Chase as well. He moved from 11th to ninth in the standings.
Logano is now 13th, just seven points and one spot behind Martin Truex Jr. for the second wild card.
Sunday's race began with 10 of the first 17 laps under caution. There were nine cautions in all, and Logano and Kurt Busch led for 94 of the 200 laps — nearly half the race.
The 54-year-old Martin emerged late, making a bid for his first Cup win since 2009, but his fuel didn't hold up. He finished 27th.
Johnson finished 40th and is now winless in 24 Cup starts at MIS. His lost weekend began when a practice crash Saturday forced him to use a backup car and start in the back of the field. He quickly made his way into contention before the engine problem ended his day.
Logano's win gave Ford a sweep of the two Cup races at Michigan this year. Greg Biffle won in June and finished ninth Sunday.
Two of Logano's three wins have come from the pole.
Johnson still leads the standings by 41 points over Clint Bowyer.