The moves paid immediate dividends as the club turned in one of its best offensive efforts of the season.
Kelly Johnson and Edwin Encarnacion homered and ace Ricky Romero earned his fourth win as the Blue Jays defeated the Rangers 11-5.
Farrell moved Johnson into the leadoff role and Yunel Escobar down to the No. 2 spot. Adam Lind got the day off so Encarnacion batted in the cleanup spot behind slugger Jose Bautista.
The Blue Jays responded with an 11-hit attack and took advantage of their opportunities against one of the top teams in the major leagues.
"I don't want to say it was just a pure shakeup of the lineup," Farrell said. "But I think sometimes you put a guy in a different slot and all of a sudden they have a different view and maybe a fresh start and it worked out today."
Johnson hit a two-run shot in the third inning and Encarnacion added some insurance with a three-run blast in the sixth. Escobar chipped in with a three-run triple for the Blue Jays (14-11), who took two of three games from the Rangers.
"Any time you play these teams that are really good, there's a different vibe and a different feel," Johnson said. "When you beat them and you beat them in a series, it gives you a big boost. It gives you a high."
Romero (4-0) allowed six hits and five earned runs over eight innings. Reliever Joel Carreno, who was recalled from triple-A Las Vegas earlier in the day, had two strikeouts in a 1-2-3 ninth inning.
Starter Matt Harrison (3-2) absorbed the loss as Texas (17-8) dropped consecutive games for the first time this season.
Johnson's homer, his sixth of the season, hit the facing of the second deck in right field.
The Blue Jays broke things open an inning later on a two-run double from J.P. Arencibia and the bases-clearing triple from Escobar that chased Harrison from the game. Escobar later scored on a sacrifice fly from Bautista.
Both Johnson and Escobar have handled leadoff duties throughout their careers. Farrell wouldn't commit to locking them in at those spots but did say it's something the team may look to go with "for a little bit."
Johnson was asked if the switch to the No. 1 spot made any difference to him.
"Eleven runs difference today so I guess we'll stick with it," he said with a smile.
Texas scored four runs in the fifth inning but Encarnacion put the game out of reach with his team-leading ninth homer of the season. He stroked a first-pitch sinker from Scott Feldman over the wall in left field.
"Edwin is just continuing to carry us," Johnson said. "We needed to answer back and he answered back big right there."
Toronto outhit Texas 11-6 on the day. It was the Blue Jays' second straight home series victory as the club improved its record at Rogers Centre to 8-7.
Romero worked his way out of a jam in the first inning when the Rangers had runners on second and third with one out.
Mike Napoli hit a grounder to third baseman Brett Lawrie, who threw home in plenty of time to catch Elvis Andrus, who was tagged out by Arencibia after running back to third. Romero then got Nelson Cruz to ground out to end the threat.
Rangers left-fielder Brandon Snyder opened the scoring in the second inning with his first career home run, a solo shot to centre field.
Texas cut into Toronto's lead in the fifth after Romero walked the bases loaded. Andrus knocked in two runs when centre-fielder Colby Rasmus misjudged the line drive and had it sail over his head all the way to the wall.
Michael Young drove in another run with a flare to shallow right field and Mike Napoli made it a three-run game with a sacrifice fly.
"You try not to panic in those situations," Romero said. "When things are going a little sideways, you've just got to slow it down. You've just got to realize that one, you're winning the game and two, you have a defence behind you that's going to make plays.
"That's what I was able to do. I came out after that and I was aggressive."
Announced attendance was 25,123 and the game took two hours 45 minutes to play.
Notes: The roof was open at Rogers Centre despite breezy, overcast conditions. The temperature hovered around the mid-teens. ... Before the game, the Blue Jays sent left-hander Evan Crawford to triple-A Las Vegas and recalled Carreno. ... Rajai Davis got the start in centre field but was replaced by Rasmus in the fifth inning. Designated hitter Ben Francisco batted fifth and Arencibia was back behind the plate after backup catcher Jeff Mathis got the start a night earlier. ... Farrell said Davis strained his left hip flexor and is day-to-day. ... Toronto Rock forward Garrett Billings threw out the ceremonial first pitch. ... The Blue Jays will kick off an 11-day, 10-game road trip on Thursday night against the Los Angeles Angels. Brandon Morrow (2-1) is expected to start for Toronto against Dan Haren (1-1).