Neither sides' European ambitions were boosted as Remi Garde's men came from behind to seal a point through Lisandro Lopez's 76th minute leveller.
The deadlock was broken in the fifth minute when former PSG striker Mevlut Erding capitalised on some lax defending for only his fourth league goal of the campaign.
Rennes had plenty of chances to put the game to bed against a poor Lyon side, most noticeably fired wide despite being afforded the luxury of an open goal. 14 minutes from time, their profligate finishing was to be punished as Lisandro Lopez popped up to turn home a Clement Grenier free-kick as the points were shared.
The hosts were without captain Kader Mangane who opted for season-ending surgery, with Tettey replacing Tongo Doumbia in the heart of midfield, as Frederic Antoinetti retained the majority of the side that featured the previous week.
Lyon, who had recorded victories in each of their lost four games, were without the suspended Cris, Bakary Kone and Alexandre Lacazette, replacing the trio with the more youthful Samuel Umtiti, Gueida Fofana and Mohamadou Dabo in a traditional 4-4-2 line-up.
And it was les Rouge et Noir who hit the ground running inside the first five minutes. A poor clearance created an opportunity for Erding to cut into the area and firing a low effort past Hugo Lloris, to hand the hosts a 1-0 lead.
It could've been 2-0 eleven minutes later when Michel Bastos was caught on the ball, and outmuscled by Jires Kembo-Ekoko, with the latter delivering a threatening cross which beat Lloris, though failed to find the outstretched feet of Erding as the visitors breathed a sigh of relief.
Lyon were markedly poor in much of the first half, only restricted to one half-chance on goal despite retaining almost two-thirds of possession as their front line were noticeably kept at bay by the likes of Onyekechi Apam and Romain Danze.
The hosts spurned another glorious chance just before half-time. Tettey threaded a neat ball in towards Kembo who beat Dejan Lovren and the defensive line, but shot frustratingly wide under the pressure of an on-rushing Lloris as an otherwise poor half came to a close.
Rennes, who had only lost one of their last eight matches against Lyon started the second period in the same dominating manner as the first. Yann M'Vila cleverly spread play to the wing to Julian Feret whose fine cross picked out Erding in a dangerous position.
The Turkish international fired an effort at Lloris who saved brilliantly with his legs, with Tettey inexplicably powering the rebound inches wide despite a gaping goal as les Gones were left reeling.
Remi Garde's misfiring side were to be denied minutes later when substitute Jimmy Briand ran through on goal and collided with Rennes goalkeeper Benoit Costil, though stand-in referee Philippe Malige ruled otherwise as the ball trickled out of play.
Lyon finally found their attacking rhythm just before the hour and were unlucky not equalise. Briand proved a handful on the flank, and his low cross in towards Lisandro was caught in between the Argentine's legs as an alert defence cleared their lines.
Les Gones finally found the equaliser after 76 minutes, again from questionable defending, this time on Rennes' part. Substitute Grenier's free-kick picked out Lisandro who needed two attempts to force the ball into the net after the initial shot came back off the post.
Following on from the draw, Lyon sit in fourth with 50 points, six behind Lille who occupy the final Champions League qualification spot and host Auxerre next. Rennes, who have not won any of their last four league games visit Evian and occupy sixth position, amassing 45 points.