Unai Emery's side were on a high following a midweek success over leaders Real Madrid, but Celta ended that euphoria with the successful spot-kick three minutes from time.
Celta came into the match on the back of two successive defeats, but were on top in the early stages with chances for both Michael Krohn-Delhi and Rafinha.
Sevilla, in contrast, took over 20 minutes to settle before Kevin Gameiro fired over the bar and then saw a right-footed strike parried by home goalkeeper Yoel.
Javi Varas then had to be alert at the other end, with Augusto Fernandez pumping in a cross for Brazilian striker Charles, whose header was safely held by the Sevilla keeper.
Carlos Bacca gave the visiting supporters false hope their team would go ahead before the interval when his close-range header fell wide of the left post.
Celta were again the better team at the start of the second half and Rafinha drew two fine saves from Varas as the hosts pushed for an opening goal.
And they should have been in front after 65 minutes through Fabian Orellana's powerful drive which crashed back off the crossbar, much to the relief of Emery's men.
Substitutions from both sides then interrupted the flow of the game while Sevilla also lost Gameiro to injury six minutes from time.
And while the visitors were still regrouping, a charge forward from Celta resulted in Federico Fazia giving away a penalty for a handball with just minutes left on the clock.
Nolito stepped up to take the spot-kick, slotting the ball into the bottom right corner.
It was a heavy blow for Sevilla and sparked a spell of late pressure to try and salvage something from the match.
However, Yoel ensured his side would keep all three points with two great saves to deny both Nicolas Pareja and Bacca in stoppage time.