Irving and James combined for 17 points in the fourth quarter as Cleveland improved to 6-3 since Tyronn Lue replaced David Blatt as head coach on Jan. 22.
Kevin Love was out with a bruised left thigh, but the Cavaliers went ahead early in the game and never gave up the lead despite a strong rally by New Orleans in the second half.
Norris Cole scored a career-high 26 points while Anthony Davis scored 24 points with 11 rebounds for New Orleans, which has lost four straight.
Cleveland nearly blew a 15-point lead for the second straight night. The Cavaliers were ahead 54-39 late in the second quarter, but the Pelicans cut the lead to four on several occasions in the second half.
Cleveland held a 15-point lead in the first quarter Friday against Boston, but lost on Avery Bradley's 3-pointer at the buzzer.
Cole, who was 10 of 19 from the field, scored 14 points in the third to help New Orleans get back in the game. The Pelicans trailed 74-70 going into the fourth.
Irving was 11 of 21 from the field while James made 11 of 20. James' 3-pointer early in the third broke his 0-for-18 slump from behind the arc.
J.R. Smith scored 20 points, including six 3-pointers. Tristan Thompson was scoreless, but had 15 rebounds in 33 minutes.
Davis shot 13 of 22 and finished with 31 points, 12 rebounds and four steals in New Orleans' 114-108 overtime win over Cleveland on Dec. 4.
Pelicans: Cole had his number retired by Cleveland State in a ceremony Saturday afternoon. James, who was Cole's teammate in Miami, and his New Orleans teammates attended the ceremony. .... New Orleans is 5-20 and 0-7 against Eastern Conference teams on the road.
Cavaliers: Love was injured Friday night. Lue said his status is game-to-game. ... Timofey Mozgov started at center with Thompson moving to power forward. .... Matthew Dellavedova (sore left hamstring) missed his third straight game.
Pelicans: Visit Minnesota on Monday.
Cavaliers: Host Sacramento on Monday.