Hendricks stuck out 10 and walked one before Jeremy Jeffress worked around two walks in the ninth for his eighth save. After 104 pitches - including 73 strikes - Hendricks narrowly missed his fifth career shutout and his second this season.
The right-hander had pinpoint fastball command to get ahead in counts. Then Hendricks was able to mix in a much-improved curve to spin his way to another sparkling outing as the first-place Cubs moved 11 games over .500 (31-20) for the first time in the pandemic-shortened season.
''You love the way he's moving the fastball around,'' Cubs manager David Ross said. ''That's such as key for him. And the breaking ball was really good tonight. You hadn't seen that in awhile.
''I thought his whole arsenal was good tonight.''
Hendricks (6-4), who lowered his ERA to 2.93, is known for hitting spots with his fastball and changeup. A better breaking ball gives him an added weapon and makes him more than ''a two-pitch pitcher,'' he said.
''(The curveball) all year has been the best it's been for me in my career,'' Hendricks said. ''Tonight was one of the best. When I see an opportunity to throw it, I'm not shying away from it anymore.''
Willson Contreras' sharp RBI single in the first accounted for the only run off the 40-year-old Hill, who walked the first two Cubs batters and then settled in on a clear, chilly night at Wrigley Field with the wind blowing in.
Hendricks retired 12 Twins hitters in a row during a stretch from the second until Josh Donaldson's bloop single with two outs in the sixth.
The Cubs' lead in the NL Central is five games over St. Louis, which swept a doubleheader from Pittsburgh.
The Twins remained three games behind the first-place White Sox in the AL Central.
Hill (2-2) allowed one run and three hits while walking two and striking out five in seven innings. Contreras had two of the three singles off Hill, with one coming on a bunt.
''We got really good pitching tonight,'' Twins manager Rocco Baldelli said. ''Rich went out there and did a heck of a job. We weren't able to scrap anything together.''
Hill stopped short of saying he felt his best this season, but said his 16 years of major league experience allowed him to keep pace with Hendricks and all-but shut down the Cubs.
''If I haven't figured it out by now then I shouldn't be pitching,'' Hill said. ''But right now being able to go out there and use that experience and change arm slots, change angles with the breaking ball... and I mean that's a really good team.''
Caleb Thielbar relieved to start the eighth.
Hill walked Anthony Rizzo and Kris Bryant to start the game. Rizzo scored on Contreras' line single to give Chicago a 1-0 lead and Bryant raced to third.
The next hitter, Kyle Schwarber, hit a sharp grounder to Josh Donaldson at third.
Donaldson tagged Bryant for the first out at third after the Cubs star got caught off the bag.
That quelled the rally. Hill retired 16 of the next 17 Cubs hitters, with Contreras' bunt single creating the only baserunner in the stretch.
Jeffress walked Byron Buxton to open the ninth, but Donaldson followed by hitting into a double play. Nelson Cruz walked with two outs, but Jeffress fanned Eddie Rosario to end it.
Hill's 2-2 slow curve struck Schwarber just above his right elbow with two outs in the third. Schwarber was ready to take first, but home plate umpire Angel Hernandez gestured with his elbow in the air, called the pitch Ball 3 and discussed it with Chicago manager David Ross. Schwarber returned to the batter's box and struck out looking.
Twins: Reinstated C Mitch Garver and started him behind the plate on Friday. Garver missed 27 games with strained rib muscles and will be one of three catchers on Minnesota's roster down the stretch, joining veteran Alex Avila and promising rookie Ryan Jeffers. To make room, Minnesota optioned C/INF Willlians Astudillo. ... The Twins placed RHP Jake Odorizzi (right middle finger blister) on the 10-day-IL retroactive to Sept. 17. Manager Rocco Baldelli hopes Odorizzi (0-1, 6.59) will be able to start again before the end of the regular season. To fill Odorizzi's spot, Twins recalled RHP Sean Poppen from their tax squad.
Cubs: Manager David Ross said LHP Andrew Chafin (sprained left index finger) and LHP Jose Quintana (lat strain) are ''extremely close'' to returning. Chafin threw a bullpen session Friday and Quintana is schedule to toss a simulated game Saturday.
UP NEXT: Twins RHP Michael Pineda (1-0, 3.57) takes the mound on Saturday night against Cubs RHP Alec Mills (5-3, 3.93). Mills tossed a no-hitter last Sunday at Milwaukee in his previous start, just his 15th in the majors.
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