Kyle Seager drove in two runs for Seattle in a game that lasted 4 hours, 7 minutes.
"Probably the best word I can probably think of is very draining," Seattle manager Lloyd McClendon said.
Boston stranded 15 runners and was 6 for 19 with runners in scoring position.
"We had a number of opportunities we created for ourselves once again," Boston manager John Farrell said. "For us to snap out where we are, this is going to come from us on the mound."
Dominic Leone (7-2) worked 2 2-3 innings of hitless relief for the win. Fernando Rodney escaped a bases-loaded jam in the ninth for his 38th save and the Mariners' pen held Boston to one run over 6 2-3.
In Saturday's victory, Seattle's relievers gave up just two hits in 5 1-3 innings of scoreless work.
Will Middebrooks had a two-run double and drove in three runs for Boston, which is on its worst stretch since losing 10 straight in May.
Trailing 5-3, Seattle scored a run in the fourth and took the lead with two in the fifth against Allen Webster (3-2). Ackley tied it with his triple. He scored the go-ahead run on a sacrifice fly.
Middlebrooks' two-run double had given Boston a 5-3 lead in the third and chased starter Hisashi Iwakuma, who gave up five runs on six hits over 2 1-3 innings, his shortest start of the season.
Iwakuma entered with a 17 2-3 innings scoreless streak, but that ended four batters into the first.
Webster was tagged for six runs on eight hits in 4 1-3 innings.
"Overall I thought I had good command of my pitches," he said. "I just left them over the middle of the plate."
Both teams scored three runs in a first inning that lasted 42 minutes.
Copyright by STATS LLC and The Associated Press
BOSTON, MA - AUGUST 24: Hisashi Iwakuma #18 of the Seattle Mariners pitches during the first inning against the...