Zunino broke the scoreless tie leading off the fifth inning, taking Santana's first pitch deep to left field.
"He has some thump in that bat," Wedge said. "He will have to continue to learn how to hit, but you saw a glimpse there of what he is capable of."
The blast sparked more scoring for the Mariners. With one out, Brad Miller doubled and Nick Franklin walked.
With Seager at the plate, Santana's pickoff attempt to second ended up in center field, putting runners on second and third. Seager then laced a double down the right field line to give Seattle a 3-0 lead.
The Mariners added a run in the seventh. Dustin Ackley led off the inning with a double, ending Santana's night.
Miller pushed a bunt up the first base line and reliever Will Smith's throw to first baseman Eric Hosmer was wide, allowing Ackley to score.
The Royals' best offensive chance came in the fifth, when Mike Moustakas doubled with one out and took off running when Jarrod Dyson hit a line drive which looked as if it might reach the outfield.
Instead, Miller at shortstop timed his jump and snared the ball, then jogged to second to double off Moustakas and end the inning.
NOTES: Seattle manager Eric Wedge said before the game he feels like he's "hanging out there" with little clarity regarding his future with the organization. Wedge's contract — originally a three-year deal — expires after the season and Wedge indicated he's been given no word about whether he'll return for a fourth year. ... Seattle has hit 183 home runs this year, tied with Toronto for second-fewest in the major leagues. ... The last time Kansas City was shut out in back-to-back games was May 22-23, 2009, at St. Louis. ... Seattle's last back-to-back shutouts came on April 21-22, 2011, against Oakland. Wednesday was the Mariners' 14th shutout of the season, the second-best mark in team history. Seattle had 15 shutouts in 2003.