Rodgers shot an even-par 71 to claim medalist honors on the final day of the Prestige at PGA West, finishing the 54-hole event with a 9-under 204 on Wednesday in La Quinta.
Stanford won the team title at PGA West's Greg Norman Course by surviving a final-day charge by Washington, which narrowed a 14-shot deficit with a final-round 14-under to finish two shots behind the Cardinal, which finished with a team score of 831.
Rodgers held off Arizona State's Max Rottluff, who was 4-under on the day and finished at 8-under for the tournament.
Joining Rodgers in the top-10 were teammates Cameron Wilson, who tied for fourth at 6-under, and Jim Liu, who was tied for seventh at 4-under.
The win was the seventh in less than three seasons for Rodgers, who is now tied for second with Joel Kribel for career victories by a Cardinal player. The pair trail only Tiger Woods' 11 career wins.
"I'm really excited for the team to pick up our second win of the season, and hats off to Washington for a solid round to finish the tournament," Stanford coach Conrad Ray said. "Our guys held strong and finished well."
The wire-to-wire victory was the second win on the season for Stanford, which also captured the Erin Hills Invitational last fall. Rodgers was the individual champion at the event.
"We had contributions from all players in the lineup and it was neat to see Patrick Rodgers win another individual title," Ray said. "We're looking forward to working on a few loose ends to get ready for our next event."
Rodgers had a pair of bogeys and back-to-back birdies on 11 and 12 to finish his final round. The birdie on the par-5 12th was his third in as many circuits.
Wilson also birdied the 12th in each of his three rounds and finished with a 2-under 69 to close the tournament.
Liu was 3-under on the front and played the back nine even for his final-round 68, one stroke behind his prior round.
David Boote, who tied for 21st, was even for the tournament and Cardinal freshman Maverick McNealy from Portola Valley shared 24th-place honors at 1-over. Stanford's Viraat Badhwar had birdies on five straight holes — Nos. 8-12. Menlo School grad Patrick Grimes saved his best round for Wednesday with an even showing. Teammates Dominick Francks settled for 14-over for the tournament while Keegan English's 74 produced his best scorecard of the three-day event.
Stanford gets back to action with a trip to Las Vegas for the Southern Highlands Collegiate Masters (March 7-9).
Before the Cardinal men teed it up, the No. 5 Stanford women took a four-shot lead into the final round of the 36-hole Peg Barnard Invitational and never looked back, claiming the title Sunday over the 14-team field for the second straight season.
The team crown, Stanford's eighth such since the tournament's inception in 1995, came with a collaborative 2-over 570 (287-283). To put it in perspective, the Cardinal's score was 16 strokes better than second-place UC Davis (586).
"I'm really proud of the effort this week from our team, and they showed their depth from top to bottom," Stanford head coach Anne Walker said. "The players have been working really hard. The course has been playing tough, and we had a couple of really good teams here and were able to measure ourselves against some stiff competition.
"This was a great tournament, and we're very happy to walk away with the win."
Walker and the Cardinal were boosted from standout performances by Lauren Kim and Casey Danielson, who scorched the par-71 Stanford Golf Course for respective final-round scores of 68 and 69. The pair finished tied for second at 3-under 139. Each tallied one bogey in the final round.
Kim and Danielson were bettered only by UNLV's Dana Finkelstein, who went 69-68 to win the tournament at 5-under.
Defending champion Mariah Stackhouse of Stanford tied for fourth with a 1-under 141 (70-71), including a 2-under showing on her final back nine.
Quirine Eijkenboom's 153 (78-75) was good for a share of 38th while Stanford teammate Mariko Tumangan (76-79) tied for 47th.
Playing as individuals, Marissa Mar (t-35th), Danielle Frasier (t-53rd) and Jisoo Keel (t-68th) wrapped up the spring opener with solid outings.
Stanford will travel to the UC Irvine Invitational (Feb. 24-25) in Santa Ana.