The Cubs added five runs in the eighth on a solo home run by Jorge Soler, an RBI single by J.C. Boscan, a sacrifice fly by Steve Clevenger and a two-run home run by Christian Villanueva. Villanueva now has three hits this spring, and all three have been home runs.
Wood followed Scott Feldman, and gave up one hit and walked three over four scoreless innings, striking out six.
With one out in the Padres' third, Jeff Decker reached on an error by shortstop Alberto Gonzalez and Travis Buck was hit by a pitch, with both scoring on Mark Kotsay's double into the right field corner. Kotsay has hit safely in five of six games.
The runs came off Feldman, who was making his third spring start. The right-hander gave up four hits over three innings and did not walk a batter.
Padres second baseman Jeff Gyorko helped out starter Jason Marquis in the fourth. The Cubs had two outs and a runner at first when Navarro hit a grounder that Gyorko fielded on the grass behind second and was able to throw in time to get the catcher.
Marquis departed after four scoreless innings, holding the Cubs to just two singles.
San Diego's Andrew Cashner, who was the Cubs' No. 1 pick in 2008, made his first spring appearance and retired the side in the seventh. He had been sidelined since cutting a tendon in his right thumb in a hunting accident in December.
Up next: Tyson Ross, one of the top candidates for the fifth starter slot, will start against Oakland -- the team that drafted and developed him -- on Monday. Ross was traded from Oakland to San Diego in November. Sean O'Sullivan, Brad Boxberger and closer Huston Street are also expected to pitch on Monday.
Carrie Muskat is a reporter for MLB.com. She writes a blog, Muskat Ramblings, and you can follow her on Twitter @CarrieMuskat. This story was not subject to the approval of Major League Baseball or its clubs.