The Tigers stretched their lead in the AL Central to 8½ games over the second-place Indians.
The Tigers were without Cabrera due to irritation of the abdominal area.
The slugger left the two previous games early and has been hampered by a strained left abdominal for more than a month. He is day to day.
"Cabrera's huge. Everybody knows Cabrera's a good hitter and we're better with him in the lineup," Infante said. "But we've got a good team, we've got good hitting, we've got everything, good starters. We're a great team. We've got everything."
Infante hit a three-run homer in the second and added a two-run shot in the sixth for Detroit, which has beaten Cleveland seven in a row and 18 of the past 22.
"I've been trying in BP, try to hit line drives. Sometimes I make a lot of fly balls. Try to work with my top hand, that's helped me a lot.
"The second one was a good cutter, he threw a good pitch. That's why I say I'm working my top hand and try to hit line drives."
Cleveland outfielder Nick Swisher tried to explain the team's struggles against Detroit.
"Sometimes a team got your number," he said. "Just got to take it on the chin and keep moving. Keep fighting, that's all we can do."
Tigers starter Anibal Sanchez (12-7) got the win. He allowed three runs and six hits in 6 2/3 innings, walking one and striking out five.
Sanchez was replaced by Drew Smyly after Gomes' home run with two outs in the seventh made it 6-3.
Smyly got the final out and Jose Veras pitched the eighth, allowing Santana's inside-the park, two-run homer to make it 6-5.
Tigers center fielder Austin Jackson tried to catch Santana's drive to the wall by leaping as he raced back.
He got his glove on the ball, but it came out as his arm hit the wall. Jackson slumped to the ground, appearing to favor his glove arm. Santana circled the bases for his 17th homer.
Jason Kipnis, who had doubled, also scored.
Jackson remained in the game after Detroit trainer Kevin Rand and manager Jim Leyland came out to check on him.
"Just kind of jammed my shoulder a bit and knocked the wind out of me a little bit." Jackson said. "Once I caught my wind, I was all right."
"They kept coming at us," Indians manager Terry Francona said. "We fought back, which was good to see, but they just kept scoring."
Kazmir (7-7) gave up four runs and seven hits in five innings.
Outfielder-DH Jason Kubel, who was acquired from Arizona on Friday, joined Cleveland on Saturday. To make room for Kubel on the roster, the Indians optioned right-hander Carlos Carrasco to Triple-A Columbus. He will be recalled on Tuesday. ... Detroit recalled the contracts of left-hander Phil Coke and infielder Hernan Perez from Triple-A Toledo and sent right-hander Jeremy Bonderman to the same team. The Tigers also optioned right-hander Luke Putkonen to Class A Lakeland. Bonderman will be recalled to Detroit on Tuesday and Putkonen will return to the major league team on Monday. ... Sunday afternoon's series finale will feature Justin Verlander (12-10, 3.73) for the Tigers against Danny Salazar (1-2, 3.67) for the Indians.