Kroos put Madrid ahead in the first half with a fizzing left-footed strike and substitute Asensio added a second late on -- after Inter's Nicolo Barella had been sent off -- to make it five wins out of six in Europe so far this season.
Carlo Ancelotti's side end the group stage on 15 points, five ahead of second-placed Inter, with both in the draw for the round of 16 on Monday.
"We did well in this first phase of the competition," Ancelotti said. "Now we have to focus on LaLiga and in February we'll see what we can do in this competition.
"Inter needed to win. We scored early. It's normal that they had more possession. We were well-positioned at the back. The other team having possession isn't a big problem. You don't win games with possession, you win by scoring goals."
Madrid kicked off knowing a draw would be enough to top the group. They faced Simone Inzaghi's in-form Inter who hadn't lost since October -- and were returning for the first time to the venue of their 2010 Champions League final win over Bayern Munich.
Kroos opened the scoring in the 17th minute with his second Champions League goal of the season, firing past Samir Handanovic from outside the box, before Inter looked to respond, Lautaro Martinez and Perisic both shooting over the bar.
"Luka Jovic played very well, he helped the team in attack and also when brought out the ball," Ancelotti said. "He played well. If Karim isn't right, he'll play. We have some days now to see if Karim can recover, I think he can. Casemiro had a knock, but I think he won't have problems."
After the break, Barella wasted a promising break, shooting wildly off target, before Casemiro headed over from a corner.
Jovic tested Handanovic from a narrow angle and Casemiro saw a low shot saved as Madrid continued to create opportunities.
Inzaghi made a triple change -- introducing Arturo Vidal, Alexis Sanchez and Matias Vecino -- before Inter's hopes of a comeback were hit when they were reduced to ten men, Barella shown a red card for clashing with Eder Militao.
Asensio scored the second in the 79th minute, curling in off the woodwork from just inside the box, to secure the three points.