Sexson hit an RBI single in his first at-bat with the Yankees, and Mussina (12-6) pitched six effective innings to tie Cleveland's Cliff Lee and fellow All-Star Joe Saunders of the Los Angeles Angels for most wins in the AL.
"We looked good today. If we can look like this every day, we've got a chance," Mussina said.
Mussina was left off the All-Star team for Tuesday night's showcase at Yankee Stadium, yet he's certainly pitched like one of baseball's best this season.
The 39-year-old right-hander allowed eight singles and a double, but pitched out of trouble and did not walk a batter for the eighth time this year. Relying on pinpoint control, he has 16 walks in 20 starts spanning 113 1/3 innings.
Mussina gave up an RBI groundout to Ryan Sweeney in the first, then settled in to finish with six strikeouts despite not throwing his deceptive changeup all game.
"That's just the way it evolved," Mussina said.
David Robertson struck out all three hitters in the seventh, Edwar Ramirez worked a perfect eighth and LaTroy Hawkins tossed a 1-2-3 ninth as New York pitchers combined to retire its final 14 batters -- seven on strikeouts.
Bobby Abreu added an RBI double for the Yankees and Rodriguez (three hits) had a run-scoring single off lefty Greg Smith (5-8), handed the ball when scheduled starter Joe Blanton was traded to Philadelphia on Thursday.
"I wasn't throwing on short rest or anything, so that was fine," Smith said after the shortest outing of his brief career. "There was a little bit of rust, but I'm not going to make excuses. I just didn't have it tonight."
The A's, who won six of their previous seven at Yankee Stadium, have lost three straight overall for the first time since dropping four in a row May 28-31.
New York, which began a stretch that includes 13 of 16 games at home, equaled a season high by winning its fifth consecutive home game.
Looking for another second-half surge to match last year, the Yankees scored six runs with two outs. They hope Sexson can provide some pop from the right side against left-handed pitching, and he delivered immediately with a two-out RBI single in the first that tied it at 1.
"It felt good," said Sexson, released by Seattle last week. "The hardest part was not seeing a pitcher for nine days."
That certainly didn't hinder him.
"He's a guy who's done a lot of good things in his career and we believe he's got a lot left," New York manager Joe Girardi said.
Cano followed with a single to right and Rodriguez barreled into catcher Kurt Suzuki -- a clean collision -- while trying to score. Suzuki, however, held onto Sweeney's strong throw for the third out.
Cano, hoping to rebound from a disappointing first half, put the Yankees up 4-1 by driving a 1-2 pitch to right-center with two outs in the third for his first homer since June 27.
It was his first shot at Yankee Stadium since May 8 against Cleveland.
"It should be a great second half for him," Girardi said. "He's a career .330-plus hitter after the All-Star break. Some hitters just take longer to get going."
That was more than enough for Mussina, who improved to 11-3 with a 3.00 ERA in his past 16 starts with career win No. 262. His 12th win of the season surpassed last year's total.
"We were swinging the bats well at the beginning, but then he started hitting spots and then they exploded on us offensively," said Oakland shortstop Bobby Crosby, activated from the disabled list before the game.
Rodriguez's solo shot in the sixth was his 20th this season and the 538th of his career.
Oakland won the opener of its previous nine series, since a June 10 loss to the Yankees. ... The A's play 41 of their final 67 games on the road. ... It was Rodriguez's 40th homer against Oakland, most among active players. ... Mussina improved to 18-10 in 35 career starts against the A's. ... The Yankees improved to 10-3 against AL West teams. ... After striking out six in three innings, New York relievers have a 1.51 ERA in their past 17 games with 53 strikeouts and 17 walks. ... Sexson became the sixth player to start at first base for the Yankees this season. ... Oakland scored one run or less for the 25th time this year, including three times in four games against the Yankees. ... Cano's homer was the first Smith has allowed to a left-handed batter in the majors.