The visiting side had most of the best chances, but was thwarted by a goalkeeper in great form.
Benfica held on for its first point of this season's UEFA Champions League after a 0-0 draw at Monaco, despite ending the game with 10 men.
Jorge Jesus' men are once again dominating matters in the Primeira Liga but were frustrated by the hosts at the Stade Louis II in a dreary Group C encounter on Wednesday.
The Lisbon club enjoyed the better opportunities on the Cote d'Azur, however an inspired goalkeeping performance from Danijel Subasic kept Benfica at bay. Subasic pulled off a number of fine saves in the second half before Benfica center back Lisandro Lopez was sent off for a rash challenge on Joao Moutinho.
That dismissal had little impact on the game, though, as the two teams played out a stalemate that preserves Monaco's unbeaten start to the competition.
The draw leaves Benfica bottom of the group with just one point to its name ahead of the return clash at the Estadio da Luz in two weeks.
Meanwhile, Monaco is second on five points, one behind a Bayer Leverkusen side that went top with a 2-0 win over Zenit.
On his return from an ankle injury Dimitar Berbatov proved an early source of inspiration, presenting Lucas Ocampos with an open goal in the fourth minute, only for the Argentine winger to fire high over the crossbar from inside the six-yard box.
That chance was the best of an uninspiring first half that proved to be a costly one for Monaco as Berbatov's comeback was cut short, the former Manchester United man forced off in the 34th minute and replaced by teenage forward Anthony Martial.
Benfica offered little as an attacking force in the opening period but came close to breaking the deadlock in the 39th minute as Lima was brilliantly denied by Subasic from close range, the Croatian blocking the Brazilian's effort following a superb right-wing cross from Talisca.
Martial shot narrowly wide after the restart but once again the hosts were grateful to their keeper from maintaining parity as Subasic denied Nicolas Gaitan netting a wonderful individual goal.
Gaitan cleverly worked his way into the penalty area and unleashed a vicious half-volley that Subasic was equal to as he parried the ball out for a corner.
Jesus' team was the better side for most of the second half, yet it found a shot-stopper in magnificent form in Subasic, who preserved his clean sheet again in the 67th minute, keeping out Eduardo Salvio's low drive.
The game turned in Monaco's favor in the 76th minute when Lopez flew in over the ball on Moutinho, leaving Polish referee Szymon Marciniak with little choice but to brandish a straight red card.
Monaco, though, could not capitalize on its numerical advantage and was left to settle for a somewhat underwhelming point, although a similarly defiant display from Subasic in a fortnight's time should stand the French side in good stead to seal progression from an evenly matched group.