Bloomquist advanced to second on the throw home, then scored when catcher Austin Hedges, attempting to nab Bloomquist at second, threw the ball into the outfield, allowing Bloomquist to score for a 5-4 Mariners lead.
Logan Morrison was then called out on strikes to end the inning and was ejected by home plate umpire Jeff Morrow for arguing the call.
Hedges redeemed himself in the ninth, scoring Chavez from second with a single to tie the score at 5-5.
Wolf, 37, continued his comeback from 2012 Tommy John surgery with his best outing this spring for the Mariners, allowing just two hits with two walks and three strikeouts in four scoreless innings. Competing for a rotation bid as a non-roster invitee, the veteran southpaw lowered his Cactus League ERA to 4.15 in four starts.
Wolf said he's feeling stronger every day after not pitching at all last season and took another step forward with Tuesday's outing.
"You really don't want to get caught up in results [in spring games]," Wolf said. "To me it's about getting stronger and better every time out as far as the sharpness of my pitches and my strength and durability. Today I felt good about a lot of things. Obviously I want to be a little more efficient, but I felt I was able to make pitches when I needed and was able to throw all my pitches for strikes."
San Diego got 4 1/3 innings of one-run ball from Johnson, who has allowed just two runs and five hits over 8 1/3 frames over his last two starts.
Johnson, a two-time National League All-Star, signed with the Padres as a free agent for $8 million this offseason after an injury-plagued 2013 with the Blue Jays. He lowered his ERA to 3.38 in four Cactus League starts with his longest outing of the spring.
Johnson gave up an infield single to Corey Hart and a bunt base hit to Dustin Ackley in the second, but got out of that one-out jam unscathed before surrendering Brad Miller's solo blast in the third.
"Early in the game, I thought he was really sharp," Padres manager Bud Black said of Johnson. "He had good location with his fastball and threw a couple of really good sliders. And he got close to 80 pitches."
Miller, who also had a single and double in four at-bats and scored three times, is battling Nick Franklin for Seattle's starting shortstop job, but moved to second with Robinson Cano missing his fourth straight game since flying home to the Dominican Republic to deal with a personal issue.
Cano is expected back Wednesday, which will shift Miller back to shortstop to resume his battle there. He certainly hasn't hurt his chances any with a strong spring at the plate as the 24-year-old is now batting .412 with three triples, four homers and eight RBIs in 12 games.
The Padres managed only a single by Yonder Alonso and a double by Quentin off Wolf in the first four frames, and Alonso was gunned down by left fielder Ackley trying to stretch his second-inning hit into a double.
San Diego got to Fernando Rodney for two runs [one earned] with two hits in the sixth, including an RBI double by Jedd Gyorko. The other run came on a passed ball by catcher Mike Zunino before Rodney bore down with a runner on third with two strikeouts and a pop out.
Rodney, who signed a two-year deal in free agency to be Seattle's new closer, has allowed nine hits and seven earned runs in four Cactus League outings.
Padres closer Huston Street pitched a scoreless sixth with a walk and two strikeouts. Street has been taking things slow to rest a slight right groin pull and was making his first Cactus League appearance of the spring after throwing in a Minor League game on Saturday.
Seattle tied the game at 2-2 in the seventh on a bases-loaded sacrifice fly by Justin Smoak. But Quentin regained the lead for San Diego with his two-out double off Hector Noesi.
Up next: After missing the past four games, second baseman Robinson Cano is expected back in the Mariners' lineup for Wednesday's 1:05 p.m. PT game in Peoria against the Brewers. The season's biggest offseason free-agent prize flew home to the Dominican Republic on Friday to deal with a personal issue and is scheduled to rejoin the club on Wednesday morning. Cano has hit .609 (14-of-23) in nine Cactus League games this spring. Right-hander Blake Beavan (2-0, 2.13 ERA in four games) gets the start, with Danny Farquhar and Tom Wilhelmsen scheduled for relief appearances.