But Roberto Firmino, who had scored Liverpool's first on 21 minutes, struck a post with a penalty just before the break, shortly after Mohamed Salah had put them ahead.
Despite Liverpool dominating much of the second period, their defending again let them down and it was Sevilla who scored through Joaquin Correa.
The Premier League club had 24 shots on goal while their opponents had just seven -- and scored from the two that were on target.
Liverpool had only themselves to blame after dominating most of the first half and frequently threatening on the break in the second.
Sevilla scored from their first effort on goal when Dejan Lovren failed to deal with Sergio Escudero's cross from the left and Ben Yedder tapped home from close range.
But Liverpool, playing in only their second Champions League group phase in eight years, responded positively.
Georginio Wijnaldum fired wide from 20 metres, before Sadio Mane's long-range effort was saved by goalkeeper Sergio Rico.
Firmino headed just over before grabbing Liverpool's equaliser on 21 minutes with a tap-in following good work from Alberto Moreno.
Emre Can squandered yet another chance for the home side before Salah eased any raw nerves with Liverpool's second - a shot from 25 metres that took a wicked deflection off Simon Kjaer.
Four minutes before halftime Liverpool had an opportunity to put the game beyond the Spanish when Nicolas Pareja fouled Mane and Firmino stepped up to take the penalty.
He sent Rico the wrong way but his shot struck the post and bounced to safety.
It looked like it would not matter as Juergen Klopp's team continued to take the game to Sevilla after the break.
But more shoddy finishing let them down, and as Sevilla came back into the match, Anfield grew more nervous.
With his team chasing the game, Sevilla coach Eduardo Berizzo was sent to the stands for preventing Liverpool's Joe Gomez from taking a quick throw-in.
Sevilla's persistence was rewarded when Correa was given plenty of time to recover after miscontrolling the ball and shot beyond Loris Karius for the equaliser.
Philippe Coutinho received a standing ovation from the Anfield faithful when he came on as a substitute on his first appearance since asking for a transfer.
And things went from bad to worse for Liverpool when Gomez was sent off for a second booking in stoppage time.
(Reporting by Neville Dalton; Editing by Toby Davis)
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