CLEVELAND, Ohio -- Away from the TD Garden in Boston, Cavaliers point guard George Hill looked right at home once again.

Shaking off his road struggles, Hill gave the Cavaliers the scoring boost needed to complement LeBron James and help overcome Kevin Love's early-game injury.

Hill scored 20 points, his Cavaliers playoff high, on 7-of-12 from the field and 6-of-6 from the free throw line to go with three rebounds and three assists.

He opened the game with the aggressiveness head coach Tyronn Lue has been demanding, pulling up for jumpers off the high pick-and-roll and driving into the teeth of the Boston defense repeatedly. He also brought the energy on the defensive end, pressuring Boston's ball handlers and doing his part to hold them under 100 points once again.

"I think he trusts me. He kind of lets me go," Hill said of Lue's message. "Other than just saying be aggressive. But I can't blame anybody. I was never at that point to say it's this guy's fault or it's this because I can't do this. I take all the blame for it, and the way I've played on the road is unacceptable. As a player, I've got to be better."

On a night James delivered another magnum opus, making sure the Cavaliers' season wouldn't end and giving the home fans another memory in what could -- emphasis on could -- be the final time they see him at Quicken Loans Arena this season, the Cavs wouldn't have crossed the finish line without Hill's contributions.

The switch-heavy Celtics forced the Cavs to play plenty of one-on-one again. But Hill made enough plays to break through and let James have a few possessions off to get his wind so he could deliver repeated daggers in the fourth quarter while pounding his chest to the adoring crowd.

James thrusting the team on his shoulders is certainly a nice option, one that no other team possesses. Still, Cleveland's best formula this postseason has been balanced scoring, giving James just enough support. When four players reach double figures, the Cavs are 9-1 this postseason.

Hill was the de facto second option during the 109-99 win, playing Love's usual role, as he was held out for precautionary reasons while being evaluated for a concussion following a nasty collision with Jayson Tatum midway through the first quarter. Jeff Green (14 points) and Larry Nance Jr. (10) also reached the double-digit mark.

Prior to the game, Lue spoke about his team being much better on offense at home in this series. He spoke about the role players being more comfortable.

That trend continued, especially for Hill.

In three games in Boston, Hill totaled just 15 points. In the three games at The Q against the Celtics, Hill has averaged 14.6 points.

It's an oddity for a playoff-tested veteran, of course, but the Cavs weren't complaining Friday night. They needed that kind of effort, as the Celtics kept fighting back in the second half, getting within three possessions on a few different occasions.

The question now for Hill is whether he can carry his sizzling offense, the attack mentality, to Boston for Game 7 on Sunday night.

Perhaps he's pinpointed the solution to his road woes. It's his pregame meal. And not just any meal. Three barbacoa tacos with guacamole from Chipotle.

"I'm up two games -- well, the three games here, that's what I ate before the game," Hill said. "I'm for sure going to find a Chipotle in Boston, I'll tell you that."

Fueled by Chipotle, Hill played the supporting role in this Cavaliers story. He's now one win away from the final chapter he's been seeking since joining the Cavaliers in February: His first shot to play for an NBA championship.

"I didn't think I would get this opportunity," Hill said. "To get this opportunity I think is a once in a lifetime. You've got to take advantage of it. I have to focus and try to do the same things that I prepared today to take into Sunday."