Rivera's big blast came in the fifth inning, when he barely cleared the wall in center field on a three-run shot that gave the Padres a 5-3 lead.
"Once I was going down to first base," Rivera said, "I saw that [Giants center fielder Angel] Pagan was going back and back; I realized that it was gone. It's a good feeling and it's good for the team. We need this one and hopefully a lot more to come."
Rivera also ripped a two-run double down the left-field line in the fourth to open the game's scoring, becoming the first Padre to record five RBIs at AT&T Park. Not bad in two at-bats against Bumgarner, a pitcher he had never faced before.
After the game, Rivera was quick to praise hitting coaches Phil Plantier and Alonzo Powell for showing him video of Bumgarner and giving him a scouting report. It marked his first home run since May 19, 2011, and his first three-run dinger since June 26, 2005.
"I was a little off," Bumgarner (2-3) said after lasting just five innings. "I have to figure out what it was and work on it, get it fixed before my next start. My command obviously wasn't very good."
The six runs also matched a season high for the Padres, who have scored an MLB-worst 75 runs through 27 games (2.78 average).
"You never know who's going to be the guy on a certain night that's a big part of the victory," Padres manager Bud Black said. "Tonight it came from Rene Rivera. And I thought he did a good job of handling the pitching. That was a hard-fought game on both sides."
Ultimately, Rivera's quintet of RBIs stood the test against San Francisco's offense, which tagged Ross for four runs on eight hits and two walks in 5 1/3 innings.
Ten days after shutting out the Giants across eight innings in San Diego, Ross faced the minimum through three innings. He was also helped out immensely by a defense that turned a double play in both the first and second innings after he let some early runners reach base.
"You know what they say," Black said. "A double play is a pitcher's best friend. We saw that tonight with Tyson."
San Francisco eventually got on the board with Hunter Pence's RBI triple in the fourth to right-center, before Michael Morse hit a two-run single later in the inning to give the Giants a brief 3-2 lead. Ross would also surrender a solo shot to Giants second baseman Brandon Hicks in the fifth, but did enough to earn his third win of the year.
"It was definitely a battle," Ross said, adding it was nice to get a win in his native Bay Area. "My offspeed was inconsistent, left some sliders up in the zone that they hit hard. Just a battle out there."
San Diego -- currently dealing with injuries to key hitters like Chase Headley, Seth Smith and Carlos Quentin -- was also without starting second baseman Jedd Gyorko (paternity leave) on Monday. Tommy Medica (1-for-3, walk) was called up in Gyorko's place while Alexi Amarista (1-for-4, double, walk, RBI) started at second, and both players scored two runs on the evening.
"It's great, man. This team's got a lot of heart," Ross said of the short-handed win. "It's going to be nice to get all of those guys back in the lineup, but we're not going to lay down for anyone."
Once Ross was done, he handed the ball off to San Diego's stellar bullpen, which turned in 3 2/3 innings of scoreless relief to lower its MLB-best era to 1.94.
Upon hearing that his club still leads the league in bullpen ERA, Black rapped his knuckles on his desk and said, "Is that right?"
Huston Street closed out the ninth to earn his 10th save in 10 tries, second only to Milwaukee's Francisco Rodriguez (12). Despite a beat-up roster and underperforming offense, San Diego (13-14) is 2 1/2 games behind San Francisco (15-11) for first place in the competitive National League West.