Morrison called Monteith a brother and expressed his sadness at the actor's death, the New York Times reported.
The 'Glee' teacher also changed his opening song to an a capella version of "What I Did for Love," from 'A Chorus Line'. The song was performed by Lea Michele, who was dating Monteith at the time of his death, during Glee's second season.
Morrison told the crowd that he felt "awkward" going ahead with Sunday's performance but said he would continue "in Cory's honour."