Sevilla scored first and last at Anfield in a game that ensures the group remains wide open after Matchday 1.
Elsewhere Spartak Moscow and Maribor also played out a draw to leave all Group E sides on one point.
The reds welcomed back Philippe Coutinho off the bench late in the second half but he was unable to make the difference in a game that saw the reds miss the penalty that could have given them a 2 goal advantage.
Pre-match and Jurgen Klopp shuffled his defence. Karius, Lovren and Gomez coming in to replace Mignolet, Klavan and Alexander-Arnold.
But within 5 minutes it was looking like a bad decision. Dejan Lovren lunged at a cross he would have been expected to clear and Wissam Ben Yedder poked home. Sevilla 1-0 up and Anfield in shock.
As it happened: LFC 2-2 Sevilla
The reds dominated the majority of the rest of the half and a wonderful move saw the reds equalise. Moreno and Henderson put together a 1-2, and then Moreno found Firmino to tuck it away.
The reds went ahead thanks to Mo Salah's pressing. He won the ball back inside the Sevilla half, turned and fired a shot goalbound. It took a wicked bounce of Simon Kjær's boot and looped over the goalkeeper. 2-1 up with a little bit of fortune.
There was more to come - Sadio Mane was held back as he tried to run into the area and the ref signalled for a penalty - not the first time the Sevilla right back had been involved in some foul play.
Up stepped Roberto Firmino but his shot smashed off the post. A great chance for 3-1 denied.
In the second half Wijnaldum saw a powerful low drive saved by the keeper, and there was other fine attacking moves from the reds that just broke down with a sloppy final ball.
Roberto Firmino even got in the way of a Emre Can shot from the edge of the area. It was that kind of night.
The Sevilla coach was bizarrely sent to the stands after twice refusing to give the ball back to Joe Gomez - throwing it along the touchline.
Video: Highlights of the match
He would get the last laugh though when in the 72nd minute Joaquin Correa powered through the reds porous defence to give his side an equalising goal.
Even though the reds brought on Coutinho, Sturridge and a very late arrival for Oxlade-Chamberlain they couldn't get the winner.
Sevilla arguably had the best chance to win in the dying moments - when substitute Luis Muriel got the right side of Joe Gomez but put his chance wide of Loris Karius.
Seconds later Gomez collected his second yellow card and was sent off. After a year without a single red card the reds have now collected two in two games.
Maribor and Moscow played out a draw so all four sides move onto 1 point in Group E.
The reds next play away in Moscow - when Sadio Mane will return from his impending domestic 3 game ban.