Ross also surrendered two singles and two walks in the third as Cleveland extended its lead to 3-0.
"I like the fact today that he got his pitch count up," Padres manager Bud Black said about Ross. "He got close to 70. He had to work a little bit today, so that was a good endurance-builder today for Tyson."
In his fourth Cactus League outing, Indians starter Corey Kluber started out strong before ultimately giving up three runs on six hits in four innings. The Padres did not have a runner advance past second base until the fourth, when they tallied three doubles and a single to tie the game at 3.
"I might have gotten a little bit tired there in the fourth, being out there for a little while," Kluber said. "Legs might have gotten a little bit heavy, left a few balls up. Overall, I felt pretty good."
Cleveland broke the tie in the fourth when Nyjer Morgan scored on a wild pitch from Leonel Campos, but San Diego battled back on Xavier Nady's first homer of the spring.
Morgan was 2-for-5 with a single and a double.
The Indians' fifth run came in the bottom of the seventh, when Matt Carson hit a chopper to third base and Alex Castellanos' throw was off the bag, allowing Ryan Rohlinger to score.
Santana, battling for the Cleveland third base job, also made a nice leaping catch to rob Chris Denorfia of a hit and likely an RBI in the top of the third.
San Diego's Alex Dickerson had a double and his seventh RBI of the spring.
Up next: Josh Johnson will get the ball for a Thursday afternoon game against the Milwaukee Brewers at 1:05 p.m. at Peoria Sports Complex. Johnson, who signed with San Diego in the offseason, has made two Cactus League starts and has given up three runs on five hits in five innings, striking out five batters and walking one.
Joey Nowak is a reporter for MLB.com. Follow him on Twitter at @joeynowak. This story was not subject to the approval of Major League Baseball or its clubs.