Negredo double gets Sevilla back to winning ways
The Spain striker smashed a shot high into the net to level at 1-1 in the 29th minute and headed inside the near post to equalise again early in the second half, before Brazilian Cicinho struck a deflected volley for the winner.
Sevilla ended a run of two consecutive defeats to climb to 14 points from eight games, the same as champions Real Madrid in fourth, and eight short of leaders Barcelona.
Barca top the standings on 22 points, ahead of Atletico Madrid on goal difference, after Lionel Messi scored a hat-trick to guide his side to a 5-4 victory with 10 men over promoted Deportivo La Coruna on Saturday.
Radamel Falcao scored a last-minute free-kick for Atletico to triumph 1-0 at Real Sociedad, and Real overcame promoted Celta Vigo 2-0 at home.
Mallorca twice took the lead at the Sanchez Pizjuan with goals set up by Mexico forward Giovani Dos Santos, who was making his debut for the islanders.
The former Tottenham Hotspur and Barcelona player set up Pedro Bigas for the opener with a curling cross in the 26th and flicked on for Tomer Hemed to restore their advantage a minute after Negredo had grabbed Sevilla's first equaliser.
Mallorca slipped down to eighth place with 11 points.