Allen hit a finals-record eight 3-pointers in a dazzling effort for the Celtics. Rondo then took charge after Allen cooled down, racking up 19 points, 12 rebounds and 10 assists in his fifth playoff triple-double to hand Los Angeles its first home loss of the postseason.
Kobe Bryant scored 21 points while battling more foul trouble for the Lakers, who hadn't lost a home playoff game since last year's Western Conference finals.
Game 3 is Tuesday night in Boston.