Lutz, a Reds prospect who has posted multi-hit efforts in four of five AFL starts, went 2-for-4 with an RBI. Franklin, the Mariners' first-round pick in 2009, finished 3-for-4 with a pair of RBIs and two doubles as the Javelinas built a 4-1 lead by the fourth inning.
Gibson (2-0), who threw five scoreless innings in his AFL debut last week, scattered six hits over five innings, allowing a run in the fourth for his second win. The Twins' No. 16 prospect is coming back from Tommy John surgery and said his innings in Arizona will help him prepare for a full season in 2013.
"I'm feeling pretty good," he told MLB.com on Monday. "I was a little tired before I got out here, but I think my last start refreshed me a little bit. My arm felt really good, it's getting innings right now; as I get them, I'll work on stuff, but the innings I get now are going to determine how many I get next year."
Gibson threw 49 of 66 pitches for strikes, facing 20 batters. Padres right-hander Matt Stites worked around a hit in the ninth for his first Fall League save.
Lutz, batting .450 since joining Peoria, doubled home Franklin with two outs in the first and singled in the third before being erased when Orioles right-hander Mike Wright induced a double play.
Top Reds prospect Billy Hamilton went hitless for the Javelinas -- he walked and scored in the first -- but looked good defensively with an outfield assist when he gunned out George Springer (Astros) at third base in the fourth. The former shortstop is transitioning to the outfield after his record-breaking season in the Minors.
Franklin singled in the first, was thrown out trying to stretch an RBI double in the third and added a one-out double in the fifth.
Wright (0-2) was charged with three runs on seven hits and a walk over three innings. Javier Baez, the Cubs' top prospect, and Springer knocked in runs for Mesa.
Danny Wild is an editor for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.