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.
Up next for Indians: The Indians will play Sunday for the first time this spring without their five World Baseball Classic representatives, who will all leave the Goodyear Development Complex on Sunday to join their national teams. Vinnie Pestano, Cabrera, Carlos Santana, Mike Aviles and Giovanni Soto are the Cleveland players departing. The remaining Indians will travel to Glendale to meet the Dodgers at Camelback Ranch at 3:05 p.m. ET. Right-hander Corey Kluber will get the start.
Tyler Emerick is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.