Justin Morneau homered and had three RBI, and Michael Cuddyer and Luis Castillo each drove in two runs to support Santana (8-4), who easily outpitched Cubs rookie Carlos Marmol (1-2) and sent the Twins to their 12th win in 14 games.
Phil Nevin homered early and Chicago scored late on a throwing error by shortstop Jason Bartlett that followed three eighth-inning singles, but Santana struck out Aramis Ramirez with a 93 mph fastball near his neck with runners at the corners to end the threat.
The left-hander struck out six and walked one while giving up five hits.
Nevin sent an 0-1 offering from Santana leading off the second high into the seats in left field to give Chicago an early edge, prompting a fan to chuck it back in the customary ode to Wrigley Field's bleacher culture. Nevin hit long flies to center and right in his next two at-bats, but they were tracked down by Torii Hunter and Cuddyer without any trouble.
Jacque Jones, a Twins draft pick who was a regular in Minnesota's outfield the past six-plus seasons until signing with the Cubs, was the only other batter in the sagging Chicago lineup who consistently made solid contact. He hit a long fly to left and lined out hard to shortstop in his first two appearances.
Otherwise, Santana showed off his usually confounding stuff, mixing those tricky changeups well with the fastball and slider and settling in once his teammates gave him the lead.
There were thousands of Cubs fans among the ticketed crowd of 34,361, but they didn't have much to cheer after Nevin's homer. All-Star first baseman Derrek Lee -- absent the last two months with a broken wrist -- is due back soon, but manager Dusty Baker must then figure out how to use Nevin -- who has six homers among his 15 hits for Chicago since coming over in a May 31 trade with Texas.
After Cuddyer walked to start the second, Morneau drove a low-and-away pitch to straightaway center, where Juan Pierre's jump just missed a terrific catch.
In the next inning, Cuddyer drove a double down the left-field line -- high enough so it couldn't be caught by third baseman Ramirez, who made a tremendous, fully extended, diving grab of Lew Ford's liner in the previous frame.
Nick Punto scored easily and Joe Mauer came all the way around from first to make it 4-0 Twins. Morneau then slapped a single between Ramirez and drawn-in shortstop Ronny Cedeno to knock in Cuddyer.
A promising right-hander brought up from Double-A less than three weeks ago and later summoned to fill in for a beat-up rotation, Marmol settled down after the third but didn't get through the sixth -- leaving two in scoring position with two outs for Will Ohman.
Castillo hit a single up the middle to score Ford and Bartlett and give Minnesota a 7-0 lead. Marmol was charged with six hits, seven runs and four walks while striking out three in his third major league start.
The Cubs have a 10-6 lead in the all-time series against the Twins, but this was their first meeting since 2001. ... Minnesota is 8-2 in interleague games this year. ... Bartlett, batting .419, has hit in all nine games since being recalled from Triple-A Rochester.