Scotland striker Kenny Miller found the net twice in a man of the match performance, before substitute Stephen Pearson scored in the final minute with almost his first touch.
Things looked less hopeful before kick-off when Jan Vennegoor of Hesselink was ruled out with an ankle injury, forcing Gordon Strachan to recall Maciej Zurawski. Neither Thomas Gravesen nor Aiden McGeady were fit enough to return to the team.
Benfica had injury problems of their own, with Rui Costa, Giorgos Karagounis and Marco Ferreira all missing. Visiting coach Fernando Santos opted for a three-man attack, with Fabrizio Miccoli and Simao either side of Nuno Gomes.
However, it was the hosts who started the game more positively and enjoyed a sustained spell of pressure early on.
Shunsuke Nakamura and Shaun Maloney produced plenty of neat touches in midfield, but their probing failed to trouble the visiting defence and the closest Celtic came to scoring before the interval was a mis-hit cross from Lee Naylor which Benfica goalkeeper Quim had to tip over.
The better first-half opportunities fell to the visitors. Miccoli beat the offside trap but was not fast enough to reach a long ball over the top ahead of Artur Boruc, but the Bhoys goalkeeper should have had to pick the ball out of his net four minutes before the break.
The impressive Leo picked up the ball on the left flank and cut inside Paul Telfer before picking out Konstantinos Katsouranis with a pinpoint cross eight yards out. The Greek looked certain to score but instead planted his header over the bar.
The second half started in similar fashion with Celtic dominating possession but struggling to break the visiting defence open.
A stroke of luck and lightening quick reactions from Miller changed that in the 56th minute after Maloney and Naylor combined well to set up Nakamura ten yards out. The Japanese playmaker scuffed his shot but Miller pounced on the loose ball and fired home first time.
Nuno Assis almost provided an immediate response with a long-range shot which flew beyond Boruc only to strike the angle of post and bar, but Celtic soon extended their advantage with a wonderful goal.
They broke quickly after defending a corner and Maloney played in Miller with a delightful throughball which cut out the entire visiting defence. The Scotland striker took a touch before dispatching it past the advancing Quim.
Simao tried to rally Benfica in the closing stages, but they were largely restricted to long-range efforts.
The Bhoys grabbed a deserved third in the final minute when Nakamura latched on to a clever pass from Miller in the box and dispatched a powerful shot. Quim managed to parry the ball but Pearson swept home the rebound to complete a perfect night for Strachan's men.