Hellickson (7-3) allowed one run and three hits over 7 1-3 innings, improving to 6-1 with a 1.74 ERA in his last seven starts. The 6-foot-1 right-hander recorded five wins and gave up just six earned runs in 40 1-3 innings last month, earning the AL pitcher of the month award.
Joel Peralta replaced Hellickson in the eighth and yielded a two-run homer to pinch-hitter Miguel Olivo, cutting Tampa Bay's lead to 3-2. But Peralta got Ichiro Suzuki to fly out to end the inning and Kyle Farnsworth finished for his 11th save in 12 chances.
Tampa Bay scored three times in the second inning, taking advantage of a trio of bloop singles and a pair of walks off Doug Fister (3-6).
With two outs and runners on first and second, Fister allowed a flare to center by Johnny Damon that drove in a run. Damon managed to take an extra base when both middle infielders, Adam Kennedy and Brendan Ryan, chased the looping fly ball, leaving no one to cover second.
Ben Zobrist followed with a two-run single into center field.
Seattle had a chance to score in the fourth but Smoak was called out by plate umpire Darryl Cousins when he tried to score on Kennedy's fly ball to right. Smoak appeared to reach home just ahead of the tag after Matt Joyce made a strong throw to the plate.
Smoak's leadoff double in the fourth was the Mariners' first legitimate hit off Hellickson, who struck out four and walked one. Carlos Peguero earned a single in the second on a fly ball to left that Sam Fuld lost the ball in the sun and dropped in off his hip.
Peguero also doubled in the eighth and scored on Olivo's sixth homer of the season.
NOTES: Rays 3B Evan Longoria left in the fourth inning with tightness in his left side. He is day to day. ... Tampa Bay 1B Casey Kotchman returned to the lineup for the first time since Sunday, when he left with an ankle injury. He went 0 for 4. ... Rays manager Joe Maddon said Andy Sonnanstine would return to the bullpen after allowing seven runs in five innings Friday night. Alex Cobb will replace Sonnanstine in the starting rotation. ... Olivo has three career pinch-hit homers. ... Seattle's David Pauley got six outs to extend his scoreless streak to 18 innings.