Granger got off to a slow start but scored 10 points in the second quarter as Indiana expanded an eight-point lead into a 62-37 margin at halftime.
"This had to be a big win for us because we came off of a good road game," Granger said. "And it means nothing if you come back and lose."
Granger made only 6 of 21 shots in Indiana's 93-77 victory over the Heat on Monday. But Granger also had 11 rebounds and six assists, and Brandon Rush added 20 points in the impressive road win.
Back at home against James' former team, it was more of the same.
"We definitely carried it over from last night," said Rush, who scored 16 against the Cavaliers. "It was definitely big. It was definitely important for us not to let that win get over our heads. We didn't want to lay an egg."
Ramon Sessions had 15 points, six rebounds and five assists for Cleveland (5-8), which lost its third consecutive game.
"We have to understand that we have to come out with a sense of urgency and do that for 48 minutes," Cavaliers coach Byron Scott said. "This isn't even close to rock bottom. It's a good test for us. This team and this franchise have not had to play through adversity in the last seven years.
"The Pacers are a pretty good team and we played that bad."
Darren Collison scored 13 of his 18 points in the first half for Indiana (7-6), which won for the third time in four games.
"To go in and have a big win in Miami and not have any letdown is a great credit to the leadership in the locker room," Pacers coach Jim O'Brien said.
Granger scored the Pacers' first five points of the second half and Indiana extended the lead to 34 with just over two minutes remaining in the third quarter.
Granger was coming off a rough shooting night in Miami, when he went 6 for 21 from the field in Indiana's 93-77 victory Monday.
Brandon Rush had seven points in the first quarter -- including a 3-pointer from just inside half court at the buzzer -- to help Indiana build a 24-16 lead. But the Pacers really got going in the second period.
Granger went 3 for 3 from the field in the second, including a pair of 3-pointers, as Indiana outscored Cleveland 38-21 in the quarter.
Rush finished with 16 points for Indiana, which finished with 12 3-pointers, compared to three for Cleveland.
"This is definitely a loss where we can't let nights like this happen again," Gibson said. "We definitely need to understand that. We have to use nights like tonight so that we never had this feeling again."
Indiana has held its last four opponents under 100 points.
"We're very together defensively," O'Brien said. "That's a nice position when your players are talking about the defensive side of the game. They don't want to not be there for each other. That's a very positive sign early in the season."
The Pacers' victory over the Heat created excitement among fans and on the talk radio airwaves about a team that has missed the playoffs the last four seasons. O'Brien made a point of not being excited about it. "Buzz is great," he said before the game. "It's just not something I'm into." ... Scott inserted Graham into the starting lineup at forward over Jamario Moon. ... Pacers center Roy Hibbert left with a head injury in the third quarter and did not return.