Jackson, who is in camp competing for an Opening Day job as a non-roster invitee, doubled twice and drove in three runs for the Tribe. He put the Indians on the board with an RBI double to left off A's starter Andrew Triggs in the first inning, and he added a two-run double to right-center off reliever Liam Hendriks in the fourth.
"One thing that has kind of stood out in a really positive manner is his bat speed and his aggressiveness at the plate," said Indians bench coach Brad Mills. "He's always been a little aggressive -- I understand that -- but to see that aggressiveness right away, in his first few games when he plays, is pretty cool."
Mills was managing in place of Terry Francona, who traveled with a split squad to San Antonio, Texas, for exhibition games against the Rangers on Friday and Saturday.
Triggs, who is competing for a spot in Oakland's rotation, was charged with six runs on five hits in 3 2/3 innings, in which he struck out three and walked two. Abraham Almonte, Erik Kratz and Michael Martinez each delivered run-scoring hits against the right-hander.
"When you work yourself in[to] lousy counts, you can't expect to have a lot of success," Triggs said.
Indians reliever Zach McAllister started and was scheduled to work three innings, but he only lasted two after giving up two runs on five hits. McAllister surrendered a solo shot to Barreto in the first and another to Rosales in the second. Healy launched a two-run homer off Tribe bullpen candidate Steve Delabar in the fifth.
A's Up Next: The A's big four at the back end of their bullpen -- Sean Doolittle, John Axford, Santiago Casilla and Ryan Madson -- all are scheduled to pitch Friday against the D-backs at Hohokam Stadium. It will be just the second appearance each for Doolittle and Casilla. The relievers will enter behind starter Raul Alcantara in the 1:05 PT game. Listen exclusively to an athletics.com audio webcast.
Indians Up Next: In a 9:05 p.m. ET Cactus League tilt at Goodyear Ballpark on Friday, Indians ace Corey Kluber will toe the rubber against the Reds on MLB.TV. Righty Danny Salazar is scheduled to start against the Rangers in an 8:05 p.m. game, also on MLB.TV, at the Alamodome in San Antonio.
Watch every out-of-market regular-season game live on MLB.TV.
Jordan Bastian has covered the Indians for MLB.com since 2011, and previously covered the Blue Jays from 2006-10. Read his blog, Major League Bastian, follow him on Twitter @MLBastian and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.