Starting centre Jusuf Nurkic had scored 32 points and claimed 16 rebounds in the 148-144 victory but suffered a leg injury in the second overtime period after landing awkwardly.
Nurkic was carried off on a stretcher and Blazers coach Terry Stotts confirmed after the game that the Bosnian had been taken to hospital.
Damian Lillard added 31 points and 12 assists for the Trail Blazers, who ensured their sixth consecutive appearance in the post-season, while D'Angelo Russell scored 39 points for Brooklyn.
Devin Booker outscored the rest of his team-mates combined with a remarkable 59-point haul but could not prevent Phoenix Suns crashing to a 125-92 defeat at the hands of the Utah Jazz.
It was the second time Booker had scored at least 59 points in a game in his career, earning the 22-year-old a place among the sport's elite, while Rudy Gobert top-scored for play-off hopefuls the Jazz with 27 points.
The Orlando Magic sit half a game behind the eighth spot in the Eastern Conference after a 119-98 win over the Philadelphia 76ers, Nikola Vucevic scoring 28 points and adding 11 rebounds.
Elsewhere, the Memphis Grizzlies saw off the Oklahoma City Thunder 115-103, with Bruno Caboclo scoring a career-high 24 points.