Dustin Pedroia collected four hits, including a home run, to lead Boston to an 8-6 victory.
Adrian Beltre had three hits and three RBIs for the Red Sox, but was part of a ninth-inning collision that resulted in Ellsbury being helped off the field.
"He kneed me right in the ribs," Ellsbury said. "I was worried about a broken rib. I'm sure there is quite a bit of swelling in there cause it is a little tough to breathe. It didn't feel too good initially.
"They got good enough X-rays. They'll just probably blow them up on a bigger monitor [Monday] and make sure there is nothing like a minor break. There was nothing obvious on it."
Ellsbury and Beltre were chasing Mitch Maier's foul fly ball. Ellsbury remained on the grass for several minutes and isn't sure if he'll be able to play Monday at Minnesota.
"I guess [it will be] pain tolerance," he said. "I know it's going to be really sore tomorrow."
Pedroia's homer in the fourth was his third in six games. He connected in the 2009 season opener, then went 190 at-bats before his second homer on May 31.
"I don't know how many games it was, but it seemed like forever," Pedroia said. "I'm actually seeing the ball good. I usually have a tough time early. I got three pitches on the inner part of the plate and I hit them. I'm just trying to get my pitch and do damage with it. That's been my game plan."
Guillen led off the second with a drive to center and hit a three-run shot off Ramon Ramirez in the eighth to get Kansas City within two. Ramirez failed to retire any of the three hitters he faced.
"The good news is Bard and Pap did a great job," manager Terry Francona said. "The flip side is we had to get to them. We came out of the chute with a lot of energy and did some good things and then hung on for dear life."
Beltre doubled in two more runs in the fourth to give Boston an 8-3 lead.
Clay Buchholz (1-0) worked five innings for the Red Sox, yielding three runs, two earned and seven hits.
Meche (0-1), in the fourth season of a $55 million, five-year contract, allowed seven runs and eight hits. Royals starting pitchers had a 2.51 ERA in the first five games of the season.
"My outing was terrible," Meche said. "I felt fine, probably felt too good, coming out of the bullpen. My intensity was too high. I just couldn't get the ball down. My release point was off pretty much the whole day. They hit some balls up and capitalized early. I made a lot of mistakes."
The Royals optioned INF Mike Aviles to Triple-A Omaha to make room for Meche on the roster. ... Maier, who led the majors with a .475 batting average in spring training, appeared in his first game, going 0 for 2 with a walk. ... OF J.D. Drew was held out of Boston's lineup with a stiff neck. He is hoping to return to the lineup Monday at Minnesota. ... INF Bill Hall made his Red Sox debut, starting at shortstop and moving to right field in the ninth. He went 0 for 3 and committed an error in the first that led to an unearned run. ... Red Sox DH David Ortiz struck out four times, bringing his strikeout total to nine in 19 at-bats. He is hitting .111 with one extra-base hit and one RBI in five games.