"Having the success that I did really showed me that I belonged there and could compete at that level," said Paxton, who was 3-1 in four starts last season.
Cleveland starter Travis Banwart lasted just two-thirds of an inning and allowed four runs and three hits, including a leadoff homer by Abraham Almonte. Banwart left with the bases loaded, and Nick Hagadone walked Michael Saunders and gave up Franklin's two-run single.
Pinch-hitter Francisco Lindor, a 20-year-old top prospect, hit a tiebreaking double off Danny Farquhar in a three-run ninth.
"If we'd have played him the whole game, he would have had something to say about the game before that (the ninth)," Indians manager Terry Francona said. "We told the kids 'You can sit here and eat seeds and have a Coke, or you can be ready to play and go in and try to do something,' and I think you can see that he's ready to play once he gets in there."
Ryan Raburn made it 5-all with a two-run homer in a four-run seventh against Lucas Luetge.
Seattle started position players who all could be on its opening-day roster. Robinson Cano singled and scored, and Kyle Seager doubled and scored.
Indians: Banwart previously pitched one hitless and scoreless inning in spring training.
Mariners: Paxton's strong bid for the starting rotation when the regular season opens continued.
He had a long wait as the Mariners jumped out to a big lead in their half of the first inning. "I just tried to stay loose in the dugout a little bit," Paxton said. "I stayed warm. Luckily we're in the heat in Arizona."
Paxton worked on the placement of his fastball and threw more curve balls than in his previous outing.
IN THE PEN
Four Indians relievers held the Mariners to one run over seven innings, while Seattle's results were mixed.
Brandon Maurer, who made the big-league club out of spring training last year, gave up a run on two hits and walked one in two innings. Luetge, a left-hander who has 98 appearances in the majors over the past two seasons, allowed four runs on three hits in 1 2/3 innings. Another lefty, veteran Joe Beimel, enhanced his bid for a spot in the bullpen by striking out one and picking off a runner at first base in his inning of work. Farquhar took the loss.
"Danny threw the ball extremely well. We just didn't make any plays for him," Mariners manager Lloyd McClendon said.
The Mariners optioned left-hander Danny Hultzen to Class AAA Tacoma, one of several roster moves Wednesday. Hultzen is one of the club's top pitching prospects but is working his way back from offseason shoulder surgery. He will not pitch in 2014.
Seattle: Franklin and another young infielder, Brad Miller, are battling for the Opening Day shortstop spot. Franklin added a stolen base after reaching on an error in the sixth and is batting .333,
Cleveland: Raburn got four plate appearances as the designated hitter, with the Indians giving most of their regulars a day off. Raburn went 2-for-3 including his home run, and his 13 total bases lead the Indians so far in spring training.
"He leverages the ball. He uses his legs, his hands," Francona said of Raburn. "He uses the whole field. He stays inside the foul poles and the ball backspins the other way."
The Indians on Thursday send RHP Justin Masterson to the mound for his second spring training start against the Chicago Cubs in Goodyear, Ariz. The Mariners have RHP Scott Baker scheduled for his second spring start Thursday against the Chicago White Sox in Glendale, Ariz. Closer Fernando Rodney is also scheduled to pitch.