Rodgers shook off mid-round miscues that included back-to-back bogeys at the fifth and sixth and a double bogey at the 10th, his eagle at the par-five 12th giving him a big boost under the Modified Stableford scoring system in use for the event that awards points for birdies and eagles and deducts points for bogeys and worse.
His third birdie of the day put him on 32 points - one behind overnight leader Gerard, and his clutch birdie at the last was enough to put him in front as he chases the first PGA Tour title of his career.
"It was a day of resilience, for sure," Rodgers said. "I shot myself in the foot more than once today, especially in this format.
"I missed a couple of really tiny putts on the front nine. Other than those, missed a few opportunities, then made a double on 10.
"I was really super proud of the way that I was resilient and turned the round around and knew there was still a lot of points to be had."
Gerard, who is also seeking a first tour title, came into the round with a four-point lead but in tougher afternoon conditions he, too, had to overcome adversity in the form of three bogeys - including two straight at 10 and 11.
He bounced back with a chip in for birdie at the 12th and rolled in a long birdie putt at 13 to get to 33 points - but his five pars coming in didn't earn him any more points.
"I didn't hit it very well at all today," Gerard said. "I didn't really make too many putts besides the one on 13. So just a lot of a grind out there today."
American Akshay Bhatia was alone in third on 31 points after posting an eagle and six birdies in his round worth 17 points in more benign morning conditions.
The strong showing wasn't something the Californian would have predicted on the Tahoe Mountain Country Club course.
"I wouldn't say this golf course or the altitude really suits my game," said Bhatia, adding that some shots had been "super confusing on the numbers and everything."
A few adjustments helped him off the tee. More importantly, a few more putts fell to make the difference in a scoring format in which "birdie and eagles are big."
Although he finds it tricky, Bhatia said the high altitude course was a good fit for the scoring system that can reward aggression.
"You've got drivable par-fours, you've got short par-fives. So it's a great format to make a ton of birdies."
