Volquez, who will leave his club Sunday to begin his stint with Team Dominican Republic in the World Baseball Classic, lasted two innings, allowing six runs on eight hits.
Jimenez worked two frames as well, giving up five runs on seven hits.
The Indians got the scoring started in the first inning when Jason Kipnis drove in Asdrubal Cabrera after the shortstop tripled on a fly ball Jesus Guzman lost in the sun in left field.
Later in the frame, Lonnie Chisenhall plated two more runs with a single before Ryan Raburn smacked his fourth home run of the spring, a three-run blast to left field.
Raburn, a non-roster invitee, has scorched opposing pitchers to start the spring, batting 9-for-15 thus far with nine RBIs.
"It's a great start; I feel great," he said. "I'm glad to have the results, but I'm focused on making the team."
The Padres answered back in a big way two innings later, scoring seven runs and chasing Jimenez from the game in the process. Logan Forsythe highlighted the scoring outburst with two triples in the third, including one that drove in two runs.
Alexi Amarista drove in the eventual winning run in the sixth on a sacrifice fly.
Padres up next: Projected Opening Day starter Clayton Richard makes his first appearance of the spring at 12:05 p.m. PT on Sunday against the White Sox at the Peoria Sports Complex. This will be the first scheduled television game on Fox Sports San Diego. Richard, who tied his career-high of 14 wins last season, is expected to pitch two innings. Rotation hopeful Anthony Bass will most likely follow Richard and go two to three innings. Bass tossed two scoreless innings last week in his first Cactus League appearance.
Tyler Emerick is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.