Doc Rivers would have junked the final two exhibition games if he could. His guys were ready to go. Mike Brown would like another month of training camp.

And so the newly fortified Celtics are off and running in pursuit of championship No. 18. They got one thing out of the way early: with last night’s 95-89 conquest of the Cavaliers they already have won a big game on the road.

“Great win, obviously,’’ said Rivers. “We talked before the game about trying to handle their intensity early. We knew they’d come out jacked up, but not 13-2.’’

Who hasn’t seen this in an NBA game? An adrenaline-fueled home team gets off to a rocket start, in this case scoring on its first six possessions, eight of its first nine, and 12 of its first 16. They go up by as many as 14 (19-5, 21-7). It is at this point you find out what the opponent is made of.

You might say this scenario was just what - I almost hate to do this, but you know what’s coming - the doctor ordered. Might as well see what your team is made of in Game 1.

If you’ve been following the Celtics at all during the exhibition season, you know that Doc Rivers has been practically giddy on the subject of his bench. Last night we all saw why.

He subbed in a Rasheed Wallace for Kendrick Perkins, trailing 21-12. At 26-14 Marquis Daniels came in for Ray Allen, announcing himself to his new Celtics TV audience by stripping the ball from LeBron James on an iso situation just before the first-quarter buzzer. By the end of the first the Cavs’ lead was down to 7 (28-21), and by the 5:41 mark of the second quarter the game was tied at 36, as Shelden Williams and Eddie House were making their own contributions.

Kevin Garnett, replaced by Williams with 2:08 left in period one, sat for the next 9:37. When he returned the team was up by 3 (41-38), having outscored the Cavs by a 24-10 margin.

This is kinda what Doc and Danny Ainge had in mind.

And when crunch time came, and a 15-point lead (62-47) had, predictably, been whittled to 4 (83-79), the guys earning the eight-figure salaries went to work. When the Celtics absolutely, positively needed to score, Garnett banked home a spinner and Pierce turned into the 2008 playoff MVP guy and that was that.

“That was as good a team effort as you’d want to see,’’ Rivers exclaimed. “The second unit saved the game for us and the first unit won it.’’

Whatever the state of Cavalier readiness, put this down as a very satisfying win for the Celtics, who were annihilated (107-76) the last time they came here. This in fact, snapped a run of 16 consecutive Cavs home victories in this rivalry. Neither team had won in the other guy’s gym since the Cavs beat the Celtics in whatever they were calling the Garden Jan. 3, 2007.

“That was a bad loss,’’ Rivers acknowledged about the whipping his team had received last spring. “But I didn’t bring it up.’’

“Different team,’’ sniffed point guard Rajon Rondo. “Last year has nothing to do with this year.’’

It’s a team that can, and will, beat people in many different ways. They’ve got scoring punch all over the floor. They will pass the basketball. They can rebound. They’ve got a bench. And they will guard you.

That’s the aspect Rivers was most concerned with, of course. The 2007-08 champs were great, in the final analysis, because it may have been the best defensive team the Celtics ever have had. So, get this. Asked if he thinks this team could reach, or exceed, that level, the coach answered in the affirmative.

“Yeah,’’ he said, “we could be. We’ve got a lot of bodies, and we’re gonna be good. But we’ve got to work at it.’’

LeBron was quite willing to second Doc’s emotion.

“First of all,’’ he said, “they are a great team. They took us out of a lot of our sets that we have been working on in practice. They made us get into a lot of ‘hot’ situations, meaning late [shot] clock, and into a lot of one-on-one basketball.’’

This is most definitely the time you want to be playing the Cavs. You don’t want to play LeBron at any time, of course, as his 38 points demonstrated. But whatever Shaquille O’Neal is going to be for them is an issue. There was nothing magisterial about his 10-point, 10-rebound effort. Newcomer Anthony Parker, a 34-year-old vet ticketed to be a reserve but pressed into starting because of the Delonte West issue, was tentative.

He was also asleep when James penetrated at a key juncture (89-83, Boston with 53.4 seconds left) and pitched it to him in the corner for what would have been an open three. The ball wound up out of bounds. Perhaps where he’s come from superstars don’t give it up in those situations. But LeBron does, and next time, presumably, Parker will be ready.

The principals on both sides understand that this was only the beginning of a very long journey. By the next time they meet, in 121 days, we will have gone through Thanksgiving, Christmas, Elvis’s Birthday, the Super Bowl, and the Washington’s Birthday automobile sales. The Cavs will be a little more familiar with themselves by then.

As for the Celtics . . . “Before the game, we said it was a big game,’’ said Rivers. “Now that it’s over, I can say it’s just one of 82.’’

But it’s in the books as a win, and a very satisfying one, for the Celtics.

Bob Ryan is a Globe columnist and host of the Globe’s 10.0 on Boston.com. He can be reached at ryan@globe.com.