Navarro added another double in the fifth, giving him 502 hits in a Bees' uniform.
"It's a bittersweet moment," he said. "Obviously the goal is the be in the big leagues break records up there. But it shows the hard work and the dedication I've put in game in and game out. It's paying off."
Navarro, who turns 28 on May 14, played briefly with the Angels in 2011 and 2013. He is 3-for-14 with Los Angeles.
"I firmly believe he can play major league baseball," said Salt Lake manager Keith Johnson. "... At some point, whether it's our [big-league] team or not, somebody is going to get a gem."
Asked about Navarro's team record, Johnson said, "It's not necessarily something you want. You'd like to get some of those hits in the big leagues. But, at the same time, it's a testament to who he is as a baseball player and a person."
Against Albuquerque, the Bees trailed in the bottom of the third, 2-0.
Isotope pitcher Zach Lee retired the first two batters before Joc Pederson, the first baseman, booted Taylor Lindsey's ground ball.
Salt Lake made Albuquerque pay for the mistake when Grant Green walked and Luis Jimenez singled home Lindsey. Navarro followed with his record-breaking two-run double into the right field corner.
The Bees never trailed again.
Navarro finished 2-for-4 and bumped his batting average to .369 as Salt Lake won for the third time in four games.
"Just perseverance and consistency," Johnson said. "... Getting the job done is more important than what round you're drafted. He's done a great job at every level."
Navarro shrugged and said, "It's a record and it is Triple-A. It's not easy to play here. Not many people get a chance to play Triple-A. So it's a blessing and shows the time I've put in."
Bees 6, Isotopes 4
• Efren Navarro sets a franchise record for hits as Salt Lake beats Albuquerque.
• Navarro goes 2-for-4 and raises his season batting average to .369.
• After losing nine straight, the Bees win for the third time in four games.