Moss's two-run shot off starter Randy Bass (2-7) capped a five-run first inning and marked the sixth time in nine games that the A's first baseman has homered since being called up from the minors.
Josh Reddick and Cliff Pennington had two RBIs each for Oakland. The second-lowest scoring team in the American League going into the game, the A's have scored 36 runs in their last four games.
Blackley (1-2) pitched six strong innings for his first win since July 1, 2004, when he made his major league debut with Seattle.
The left-hander wound up back in the minors with the Mariners and spent time with San Francisco, Philadelphia, Arizona and the New York Mets -- he even pitched in Korea -- trying to get back to the big leagues before Oakland claimed him off waivers from the Giants.
Blackley pitched out of a jam in the first then calmed down after giving up San Diego's second run an inning later. He retired 12 of the final 14 batters he faced, finishing with three strikeouts and two walks.
Evan Scribner allowed one runner over the final three innings for Oakland for his first save.
Carlos Quentin had two hits and an RBI for San Diego, which lost for just the second time in seven interleague games this season.
Earlier in the day the A's parted ways with Manny Ramirez after the 40-year-old slugger asked for his release and the team granted his request.
Ramirez signed a minor league contract with the A's in February and served a 50-game suspension for violating Major League Baseball's drug policy last year, but remained in the minors when the ban ended on May 30. He was batting .302 with 14 RBIs in 17 games with Triple-A Sacramento when he asked out of his contract with Oakland.
Moss is no Manny but he has definitely provided a boost for the A's offense since being called up from the minors on June 6.
He homered in each of Oakland's three games at Colorado this week then put the A's up 5-1 in the first inning against San Diego with a two-run blast off Bass.
It was the first time an A's player has hit a home run in four consecutive games since Jack Cust in 2007.
The Padres cut it to 5-2 when Alexi Amarista tripled and scored on Chris Denorfia's single in the second.
Pennington doubled in Collin Cowgill in the fourth then scored on Coco Crisp's infield single, giving Oakland a 7-2 lead.
Bass (2-7), who has not won since going eight innings to beat Washington on May 15, struck out three and was charged with nine runs, seven earned.
Bass walked the first two batters he faced then surrendered a two-out double to Reddick, three batters before Moss homered. He gave up two runs in the fourth then left after giving up consecutive one-out singles in the sixth.
Brad Boxberger replaced Bass but made a critical throwing error to center field after appearing to have easily caught Cowgill trying to steal second. Kurt Suzuki scored on the play and Cowgill later scored on Pennington's single.
Notes: Oakland's 36 runs are its most over a four-game stretch since they scored 48 from June 6-9, 2004. ... Pennington celebrated his 28th birthday on Friday and has driven in at least one run on each of his last three birthdays. ... The umpiring crew of Tim McClelland, Brian Runge, Ted Barrett and Mike Muchlinski was the same one that worked San Francisco pitcher Matt Cain's perfect game on Wednesday. ... The A's signed their first-round draft pick, SS Addison Russell. The team has signed or agreed to terms with 23 of their 43 picks. ... RHP Ross Ohlendorf (1-0) will make his first start of the season Saturday for the Padres, making him the 12th starter San Diego has used already this year. That's the most since the 2009 team had 12 for the entire season. Oakland plans to call up RHP Tyson Ross (2-6) from Triple-A Sacramento to start opposite Ohlendorf. ... The Padres agreed to terms on a $3 million contract with LHP Max Fried of Harvard-Westlake H.S., the seventh overall pick in the amateur draft.