Kanter bested Sidney Wicks' Portland record of 27 rebounds set in 1975. Kanter is the fourth player with 30 rebounds in a game in the past 20 seasons, joining Dwight Howard in 2018, Andrew Bynum in 2012 and Kevin Love in 2011.
Kanter also surpassed his own career high of 26 set while he played for the New York Knicks in 2018.
The raucous sideline cheers were a fitting tribute to Kanter, who has served as both a backup and a starter this season, as needed.
"I was so happy when I looked at the bench and everybody was up, everybody was cheering, everybody was smiling, everybody was supporting their teammates. That's what we're all about," Kanter said. "That's what Blazers basketball is all about, just supporting each other."
Starting center Jusuf Nurkic was not available for the Blazers because it was the first game of a back-to-back. Nurkic had knee swelling that kept him out of a game earlier this week at the LA Clippers.
Blazers coach Terry Stotts said before Saturday's contest that Nurkic would be available for Sunday night's game at home against the Miami Heat. Kanter started in his place Saturday night.
"When you look at the effort that it takes to rebound, the persistence at both ends, the beating that you have to take, all of those things are tough to do,'' Stotts said. "And the fact that Enes is such a great guy -- you can tell by the bench's reaction, how happy the team was for him -- but to get a rebound record speaks a lot about the person's will and drive."
After the game, Stotts was asked whether he would consider starting Kanter, given Nurkic's issue with his knee. Stotts said he would consider it.
"I don't know what Nurk's minute restrictions are going to be [Sunday],'' Stotts said. "If Nurk continues to be at a 20-minute limit, I think it's something I would consider."
The Associated Press contributed to this report.