They did just that.
The Cowboys bounced back from a disappointing loss a week earlier by grinding out a 26-20 win over the Tampa Bay Buccaneers at AT&T Stadium.
"Our guys did a great job responding with our work during the week," Garrett said.
The Cowboys (12-2) moved a step closer to the NFC East title and the No. 1 playoff seed in the conference playoff. Dallas needs one win or one Giants loss to clinch both.
Elliott, the NFL's rushing leader, produced a season-high 159 yards and a touchdown on 23 carries. He broke the 100-yard mark just once in the previous four games.
Prescott snapped a stretch of three consecutive games without reaching 200 yards passing. The fourth-round pick completed 32 of 36 attempts for 279 yards, and he also ran for a score.
"Clearly, he was seeing things well," Garrett said of Prescott. "He threw the ball well. Made a lot of really good decisions."
Dan Bailey kicked four field goals for the Cowboys, including three in the fourth quarter. Bailey also missed two field-goal attempts in the first half.
The Buccaneers (8-6) had their longest winning streak since 2002 snapped at five games. Tampa Bay also fell a game behind the Atlanta Falcons (9-5) in the NFC South.
"Overall top to bottom, we did not play as well as we have been playing," Tampa Bay coach Dirk Koetter said.
The Bucs also fell behind Washington (7-5-1) in the race for the second NFC wild card. The Redskins face the Carolina Panthers on Monday night.
"We just have to keep winning and see how it plays out," Tampa Bay quarterback Jameis Winston said. "I'm going to keep fighting, and I'm not worried about not fighting. We just need to keep winning games."
Winston threw for 247 yards and two touchdowns, completing 17 of 35 passes, but he also had four costly turnovers. The second-year pro was intercepted three times and lost a fumble.
"We've got to take care of the football," Winston said. "You can't turn the ball over four times and beat a good team like this."
Bucs receiver Mike Evans was limited to four catches for 59 yards. The third-yard pro has gone three straight games with no more than four catches.
Tampa Bay came out of halftime on a mission and retook the lead 20-17 with two quick-strike touchdown passes from Winston.
The Bucs' first drive of the second half ended with Winston's 42-yard touchdown pass to Adam Humphries. Winston was rolling left and threw across to a streaking Humphries, who hauled in the ball in the end zone after it was tipped by cornerback Brandon Carr.
Winston finished off an 81-yard march with a 10-yard bullet to Cameron Brate. Both scoring drives covered at least 75 yards and were each less than five minutes.
Dallas knotted the game at 20 on Bailey's 40-yard field goal early in the fourth quarter.
Winston followed with his third turnover, helping the Cowboys go back on top. A deep throw intended for Humphries sailed on Winston, and safety Jeff Heath picked it off easily.
Despite being set up deep in Tampa Bay territory, Dallas settled for a 38-yard kick from Bailey to make it 23-20 with 9:35 remaining.
The Cowboys went into halftime ahead 17-6 thanks to a second-quarter scoring flurry.
The first Dallas touchdown was set up by a Winston turnover. Back to pass, Winston lost the ball after getting hit on the arm by Dallas defensive tackle Terrell McClain. Rookie tackle Maliek Collins recovered it at Tampa Bay's 14.
Elliott scored from the 2-yard line five plays later and celebrated by jumping into an oversized Salvation Army bucket behind the end zone. The stunt drew a flurry of flags and a 15-yard unsportsmanlike conduct penalty.
"That bucket's just sitting right there by the end zone," said Elliott, who admitted the jump was planned before the game. "It's only right someone jumps in it."
Dallas went up two touchdowns on a 64-yard drive capped by a 2-yard quarterback keeper by Prescott. It was his sixth touchdown rushing, setting a team record for a quarterback.
NOTES: Dallas was unable to clinch the NFC East after the New York Giants beat the Detroit Lions earlier in the day. ... Cowboys RB Darren McFadden, the team's leading rusher last season, was active for the first this season. He finished with three carries for 10 yards. McFadden missed the first 13 games recovering from offseason elbow surgery. ... Dallas' inactives: QB Mark Sanchez, RB Alfred Morris, DE DeMarcus Lawrence, DT Cedric Thornton, LB Mark Nzeocha, CB Morris Claiborne and S J.J. Wilcox. ... Tampa Bay's inactives: QB Ryan Griffin, WR Donteea Dye, RB Jacquizz Rodgers, DT John Hughes III, OT Demar Dotson, DL DaVonte Lambert and OL Caleb Benenoch. ... Dallas WR/KR Lucky Whitehead returned after a one-game suspension for violating team rules. He lost 4 yards on two carries, but he returned three kickoffs for 75 yards.