Monaco forward Lucas Ocampos had an open goal at his mercy but contrived to fire over the crossbar from six metres after Dimitar Berbatov rolled the ball to him in the fifth minute.
The Portuguese champions and league leaders had the better of most of a scrappy Group C game and were only prevented from taking all three points by Monaco goalkeeper Danijel Subasic and their own poor finishing.
However, they had to ride out a difficult final quarter of an hour after defender Lisandro Lopez was sent off for a studs-up tackle on Joao Moutinho, who clearly made a meal of the challenge, in the 76th minute.
Monaco, who were facing a Portuguese side for the first time since they lost 3-0 to Jose Mourinho's Porto in the 2004 Champions League final, have five points from three games and Benfica one following a bad-tempered match punctuated by niggly fouls.
"We came for the win but it was complicated with a player less," Benfica midfielder Anderson Talisca told Portugal's Sportv cable channel. "We fought hard, we played well and we were dedicated. We had the best chances but we didn't take them."
Subasic was called into action for the first time when he made an excellent point-blank save to deny Lima from Talisca's low cross into the area six minutes before the break. Monaco missed another good chance at the start of the second half when substitute Anthony Martial broke clear and fired across the face of the goal.
Benfica took control and enjoyed their best spell of the game with Nicolas Gaitan going close when he burst through the defence and was denied by Subasic from close range. The Croat then made another good save, this time with his legs after Talisca slipped the ball through to Eduardo Salvio on the right, and then did well to stop a low, long-range shot by Enzo Perez. Shortly afterwards, Perez wasted a good chance by firing over from the edge of the area following another quick Benfica break.
Lopez's dismissal changed the course of the game and Monaco nearly grabbed a stoppage-time winner when Andrea Raggi headed centimetres wide of the goal.
(Writing by Brian Homewood in Berne, editing by Pritha Sarkar and Toby Davis)
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