"It seems like when adversity hits this team, they play their best," manager Ron Washington said.
Hamilton left because of sore lower back that has bothered him since last weekend. He was already hurting when he had a leadoff double to right in the fourth, sliding headfirst into second before then scoring on a single by Nelson Cruz that got the Rangers to 3-2 before he left the game.
An inning later, the rookies at the top of the batting order put Texas ahead to stay.
Julio Borbon drew a one-out walk before 21-year-old shortstop Elvis Andrus, moved from ninth to second in the order with Young out, hit his sixth homer to make it 4-3. Andrus flipped his bat away as soon as he hit the ball, and his fellow rookie looked back laughing while trotting around the bases.
"I started jogging and smiled. It was a good feeling, especially that time of the game," Borbon said. "We try to play our game, get on base and make things happen."
An inning later, Cruz hit his 30th homer off Scott Richmond (6-8).
Texas moved within 3½ games of the AL West-leading Angels, who have lost two in a row. It is the closest the Rangers have been in the division since the same margin Aug. 9 after a win in Los Angeles. The Rangers are 2½ games behind wild-card leader Boston after the Red Sox lost at Tampa Bay.
The Rangers know they will be without Young at least two weeks because of a strained left hamstring sustained running out a grounder Tuesday night. Now, they have to worry about Hamilton, whose back has been bothering him since playing on the turf in Minnesota last weekend.
"I've been getting treatment and doing everything I can to make it feel better," Hamilton said. "It seems like the more I run, the worse it feels."
Hamilton was slow getting to his feet at second base. When he got to the dugout after scoring, manager Ron Washington asked if he was OK.
"I told him I was," Hamilton said. "I went to run out to center field and just couldn't really do it."
Texas has a day off before playing in Baltimore on Friday night. Hamilton, on the disabled list twice earlier this season after crashing into outfield walls making catches, said he was hopeful that with treatment he would be ready to play.
Rookie right-hander Tommy Hunter (7-3) allowed four runs over seven innings and had four strikeouts. C.J. Wilson retired all four batters he faced before Frank Francisco finished for his 22nd save in 25 chances -- and third in two days after getting both in a doubleheader sweep Tuesday.
Toronto wrapped up a 1-6 road trip against the Rangers and Red Sox. The only victory was 18-10 in the opener of the four-game set in Texas when the Blue Jays let an 11-0 lead get cut to one run before scoring seven times in the ninth.
"It's not good," manager Cito Gaston said.
"We've played a couple teams in the wild card. We're trying to be spoilers," Richmond said. "We're trying to stir the pot a little bit and fell short."
Richmond was pulled after walking the next two batters after the Cruz homer. The right-hander is 0-3 with a 7.27 ERA in five starts since returning from the disabled list after 30 days recovering from biceps tendinitis.
Toronto led 2-0 in the first after Adam Lind had an RBI double and then came home on a single by Lyle Overbay, who was thrown out trying to go to second on the play. Overbay's solo homer in the fourth, his 14th, put Toronto up 3-1.
Andrus saved a run on defense, even after he bobbled Jose Bautista's grounder for an error in the fourth. Andrus recovered to scoop up the ball and threw out Randy Ruiz, trying to score from second, to end the inning.
Ruiz made up for his running miscue when he led off the seventh with a homer.
NOTES: Cruz has 23 solo homers. ... Toronto SS Marco Scutaro had his third error in three games, after only four errors the first 126 games this season. His throwing error in the sixth allowed a run. ... Blue Jays rookie LHP Brett Cecil will get an extra start this season. His scheduled start Saturday at the New York Yankees was supposed to be his last, but Gaston said Cecil will also start Sept. 11 at Detroit.