Despite having slightly less of the ball, Lazio created a whopping 17 shots on goal to Celtic’s miserly six.
Lazio should have been ahead in under ten minutes, but Felipe Anderson’s header from close range bounced over the bar.
Gustav Isaksen had his own chance on the hour mark, but his shot was inches wide.
Lazio finally got the goal they were looking for in the 82nd minute when Immobile got on the end of Isaksen’s deflected shot to beat a scrambling Joe Hart.
Immobile had his second just three minutes later when he utilised the bounce of the ball to turn one defender, cut inside the second and finish past Hart again with his left foot.
Lazio last group stage match is away to Atletico Madrid. Neither sides need anything from the game.