The rest of the batting order made up for his absence, too.
David Ortiz drove in five runs and hit one of Boston's five home runs as the Red Sox pounded the Tampa Bay Rays for the second straight day, 13-5 on Saturday, a day after Ellsbury partially separated his right shoulder.
"I know Jacoby's a big part of this offense and he's a good ballplayer, great ballplayer actually," said Aviles, who had a go-ahead homer among his three hits. "But we've got to bear down and everybody's got to step up and put the pieces together and play as a team."
The game was tied 5-all until Aviles homered, starting a three-run seventh inning. The Red Sox added five in the eighth -- on a three-run double by Ortiz and a two-run homer by Cody Ross -- one day after scoring eight in that inning in a 12-2 win.
"It's not going to happen every day, but that doesn't mean that we're not going to go at it. We have good hitters," Ortiz said. "We're going to miss (Ellsbury) a lot, but whenever we can come out and produce like we did today, we've got to take advantage of it."
The outburst was more remarkable because Boston had scored a total of just 57 runs in 18 games against Tampa Bay last season.
The Red Sox rallied from a 4-0 deficit in the first inning as Clay Buchholz (1-0) settled down.
"Buch got himself in a little trouble early, obviously," Ross said, "and then just pitched a gem after that and we picked him up."
Ellsbury, last year's runner-up in the AL MVP voting, went on the 15-day disabled list before the game after being hurt trying to break up a double play.
Aviles, batting first for just the 46th time in 346 career games, led off the seventh with a homer, his first of the season, off Burke Badenhop (0-1). The Red Sox then loaded the bases off J.P. Howell on a double by Adrian Gonzalez, a walk to Kevin Youkilis and a single by Ortiz. Ross followed with a two-run double for an 8-5 lead.
Jeremy Hellickson struggled in his first start since being hit in the head with a ball during batting practice on Wednesday. He gave up five runs on seven hits in five innings and said his head didn't bother him.
"The cutter was good. I think the first two home runs were good pitches," he said. "I've just got to throw more strikes. I felt good. Arm felt good. Nothing with the head. Just made some bad pitches."
And that forced manager Joe Maddon to bring in a reliever in the sixth inning.
"The bullpen's covering a lot of innings," he said. "We've got to get deeper into the game. That's been our strength in the past."
The Red Sox cut that in half on Jarrod Saltalamacchia's two-run homer, his first, but Scott's run-scoring double in the third made it 5-2.
Then Boston tied it with two more homers -- one run scoring on Dustin Pedroia's second of the year in the third and two on Ortiz's first in the fifth.
Aviles had batted only eighth and ninth this season, but Ellsbury's injury left a vacancy at the top of the order that figured to be tough to fill.
The center fielder batted .321 with 32 homers and 105 RBIs and led the majors with 364 total bases last season. He was hurt when he slid into second base in the fourth inning trying to break up a double play and shortstop Reid Brignac landed hard on Ellsbury's right shoulder.
Boston manager Bobby Valentine gave no timetable for his return.
The Red Sox called up OF Che-Hsuan Lin from Triple-A Pawtucket to take Ellsbury's roster spot. ... The Rays optioned RHP Josh Lueke to Triple-A Durham and recalled RHP Dane De La Rosa from that team. Lueke allowed four runs on six hits in one inning of Tampa Bay's 12-2 loss to Boston on Friday. ... The ceremonial first pitch was thrown out by Bill Hogan Jr., who was born six days before Fenway Park opened on April 20, 1912. Saturday was his 100th birthday. ... Boston LF Carl Crawford, recovering from wrist and elbow injuries, took batting practice.
Though he has been up-and-down in his five starts since coming off his second stint on the disabled list, Dodgers ace Clayton Kershaw says he definitely feels healthy and thinks "the consistency's coming."
Relive the best images from the first half including James Paxton's no-hitter, Gleyber Torres' rookie charge and Mike Trout's career year.
Jefry Marte breaks his bat after Clayton Kershaw strikes him out in the first inning and then responds with a 3-run homer in the fourth inning.
Jon Lester won for the eighth time in nine starts, Jason Heyward drove in two runs and the Chicago Cubs swept the San Diego Padres with a 7-4 win on Sunday.
Before Manny Machado arrived for the All-Star Game, the Futures Game on Sunday was a who's who of prospects bandied about in trade talks for the Orioles shortstop and others expected to be moved before the July 31 non-waiver deadline.
Mets prospect Peter Alonso mashes a 2-run home run to left field that even shocks Torii Hunter from the dugout.