Benfica and Manchester United, who beat Otelul Galati 2-0 at Old Trafford, both have eight points, with Basel, who play the pointless Romanian group whipping boys next, on five and still very much in the hunt for a last-16 place.
Benfica's next game is away to United, though they can expect to finish with three points when they host Otelul in their final match which would send them through even if they were to lose at Old Trafford.
"This was not the result that we were looking for but the draw keeps us in a good position to qualify. We will go to Manchester to win the match and fight for the top place in the group," said Benfica assistant coach Raul Jose.
Jose was deputizing for Jorge Jesus, banned for one game following a red card in last month's meeting between the two in Switzerland.
Benfica burst out of the blocks with Argentine playmaker Pablo Aimar running at the Basel defence in the first minute to feed striker Rodrigo, whose shot was tipped against the post by keeper Yann Sommer.
"I feel like I am working well and hope to secure my space in the team, things have been coming out nicely for me," said Rodrigo.
The Spaniard, selected ahead of Paraguay international Oscar Cardozo, did not waste his second chance three minutes later, firing in a half-volley into the top right corner after a headed pass from Nicolas Gaitan.
Gaitan now boasts four assists in the Champions League and almost made another decisive pass after 19 minutes with a pin-point cross that found Ezequiel Garay unmarked in the area, but the Argentine defender's header flew just wide of the goal.
Having won 2-0 in Switzerland last month, Benfica were looking good for the double that would have secured their last-16 spot but Basel gradually came back into the match.
"We always kept a positive attitude but we played against a strong opponent, who passed the ball around well, it wasn't by any chance that they drew at Manchester United," Jose said.
The visitors caused most danger from their right flank and it was from there that they earned their first real chance after 32 minutes, when Fabian Frei sent a header just wide after a cross by Jacques Zoua.
Benfica failed to turn their fluid play into a second goal and Basel grew in confidence, coming close twice in the early stages of the second half before equalising after 63 minutes in a rare left-sided move.
Scott Chipperfield made a run and squared for Huggel to slot the ball in cleanly from 12 metres out.
Benfica almost regained their lead moments later when Belgian midfielder Axel Witsel put Rodrigo through in the box, but the striker had a tight angle and hit the side netting and the celebrations were put on hold.
