Santana surrendered a home run to Sammy Sosa to open the second inning. It was Sosa's 598th career homer, but it would be all the scoring the Rangers would muster a night after they routed the Twins, 14-4.
"He's a great hitter, there's no question about it," Santana said. "If you make a mistake, you're going to pay for it. I tried to throw a fastball away, and it stayed pretty much right where he wanted it."
Santana (5-4) struck out the next five batters before Ian Kinsler doubled down the left-field line in the third inning. Michael Young followed with an infield single, and the Rangers appeared to be threatening. But Mark Teixiera flied out to right field.
The Twins took to the offensive in the fourth inning. Michael Cuddyer led off with a single, and then Morneau drove Texas starter Kameron Loe's 3-1 offering over the fence in center field to give Minnesota a 2-1 lead.
Morneau, who was the designated hitter Tuesday, increased that lead to 5-1 in the fifth on a similar pitch from Loe. Luis Castillo singled, and Cuddyer walked to set up the reigning American League Most Valuable Player's three-run blast. It was Morneau's third multi-homer game of the season, and the seventh of his career.
"I don't usually like to DH, it's kind of tough," said Morneau, the regular first baseman. "But you get that hit in the first at-bat, and then you really don't have to think about it. You can just sit on the bench and relax. It was a pretty fun day."
Morneau, who ranks second in the AL with 13 homers, finished the game 3-for-4 with a season-high five RBIs.
Working with a lead, Santana proceeded to shut down the Rangers, who had erupted for 15 hits on Monday. Santana finished the night with a season-high 13 strikeouts, just one shy of his career high. The reigning Cy Young Award winner exited the game after seven innings, having surrendered four hits.
"I tried to stay aggressive the whole time," said Santana, who is 3-1 with a 1.85 ERA in five road starts this season. "I was throwing my fastballs in and out of the plate, and that helped me to throw my changeup. We stayed with our plan."
Santana led an 18-strikeout night for Twins pitchers, a club record.
Minnesota tacked on two insurance runs in the eighth, when Torii Hunter cracked a homer deep into the left-field bleachers for his 11th homer of the season. The two RBIs gave Hunter 643 in his career, moving him into seventh all-time in club history.
"I've been feeling good since August of last year," Hunter said. "It's experience, you know? You get older, you start figuring out ways to have good at-bats. I think I'm getting better as I get older. I'm actually still learning."