Ackley hit a three-run double off Alex Cobb (1-4) during a four-run fifth that put the Mariners ahead 7-2. Port Orchard native Willie Bloomquist added an RBI double in the inning.
Elias (5-4), coming off a three-hit shutout over Detroit last Sunday, was chased after giving up a two-run homer in the eighth to Evan Longoria that cut the Mariners' lead to 7-4. The left-hander allowed four runs and five hits over 7 2-3 innings.
Fernando Rodney, the former Rays closer, pitched the ninth to get his 17th save in his first appearance at Tropicana Field since joining the Mariners as a free agent in February.
James Loney homered for the Rays, who had a stopped a 10-game losing streak by beating Seattle 4-0 Friday night.
The Rays celebrated the life of senior adviser Don Zimmer before the game. Zimmer died Wednesday night at 83. Joe Torre, Jim Leyland and Tommy Lasorda, along with more than 20 family members were present.
Bloomquist, who graduated from South Kitsap High School, had an RBI single and Endy Chavez hit a sacrifice fly during the fourth. Cole Gillespie hit his first homer of the season, a solo shot in the second.
Seattle has won five of six.
Cobb gave up seven runs and 10 hits in 4 1-3 innings. The right-hander is 0-3 in four starts since returning from a strained left oblique.
Loney had a solo shot and Ali Solis drove in a run with a sacrifice bunt as the Rays went ahead 2-1 in the second.
NOTES: Seattle 1B Justin Smoak (sore left leg) and OF Michael Saunders (sore right shoulder) were both out of the lineup. Smoak entered as a defensive replacement in the ninth. ... The Rays designated reliever Josh Lueke for assignment and recalled RHP Kirby Yates from Triple-A Durham. Yates entered in the seventh to make his big league debut. ... Seattle 2B Robinson Cano singled in the fifth and has a 16-game road hitting streak. ... Rays RHP Jeremy Hellickson (elbow) and C Ryan Hanigan (hamstring) started minor league rehab assignments with Single-A Charlotte. Hellickson gave up two hits in three shutout innings against Tampa. ... Seattle RHP Felix Hernandez (8-1) and Tampa Bay RHP Chris Archer (3-3) are Sunday's scheduled starters ... First pitch is slated for 10:40am (PT).