Oakland entered the day with half that, but Derek Norris' two-run shot off right-hander Hisashi Iwakuma in the fourth inning upped it to 23.
Iwakuma allowed just one one other run in his five innings of work, a sacrifice fly off the bat of Scott Sizemore in the fifth. Overall, the right-hander surrendered six hits and walked two with no strikeouts. He also hit a batter.
Firmly entrenched in Seattle's rotation, the 31-year-old Iwakuma had given up just seven hits with no walks in 10 innings going in to Monday's contest, and he exited the game with a 3.60 ERA.
A's starter A.J. Griffin entered the day with similar numbers, having allowed just one run through five innings of Cactus League play before being tagged for five on six hits in 5 1/3 innings against Seattle.
Griffin, penciled into the A's rotation as the fourth starter, allowed just two baserunners through the first four innings without giving up a run. But in the fifth, he offered up a leadoff double to Jesus Montero, who had been robbed of a home run in the second when Coco Crisp made a spectacular catch at the wall in left-center.
Montero advanced to third on a groundout and, after Robert Andino walked to put runners at the corners, third baseman Brad Miller sent them both home with a double to tie the score at 2.
Michael Saunders' ensuing RBI base hit gave the Mariners the lead, and Seattle added two runs in the sixth on Morse's long ball and an RBI single from Dustin Ackley.
Morse, acquired in a trade with the Nationals, has had an immediate impact on the Mariners.
"He's had a real good spring for us," said manager Eric Wedge. "He knows what he wants to do up there. He's a smart hitter. He's strong. He does a good job making adjustments. That's why he's in the middle of our lineup."
Morse is now hitting .371 with 11 RBIs in 13 games, and teammate Justin Smoak upped his average to .390 with a two-hit day as he continues to bounce back from a tough 2012 campaign.
Up next: Young right-hander Brandon Maurer gets the start on Tuesday in a 7:05 p.m. PT game against the Giants at Peoria Stadium. Maurer, 22, has been very impressive this spring, and is contending for one of the final rotation berths despite never pitching above Double-A. He's scheduled to throw five innings, with closer Tom Wilhelmsen, Charlie Furbush and Steven Pryor to follow. Veteran lefty Joe Saunders is scheduled to throw in a Minor League intrasquad game at the Peoria Complex at 10 a.m.