Second-placed Atletico Madrid had reduced the lead to five points when they won the capital's derby 1-0 at the Bernabeu on Saturday, a result which now leaves Real Madrid 12 points adrift of Barcelona.
Sevilla went in front from a break down the left with full back Benoit Tremoulinas crossing to the far post where Vitolo volleyed past Claudio Bravo after 20 minutes.
Messi equalised just past the half hour with a sublime free kick that dipped over the wall and went into the top far corner.
Barcelona's winner, as they extended their unbeaten run to 34 matches, came three minutes into the second half when Messi cut the ball back to Luis Suarez who crossed into the six-yard box where Pique turned it into the net.
(Writing by Rex Gowar, editing by Ian Chadband)
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