Federico Fazio was sent off in conceding a penalty in the 20th minute and Radamel Falcao slotted home the spot-kick to open the scoring.
The game was practically put beyond Sevilla's reach with two goals late in the first half.
Emir Spahic scored an own-goal on 40 minutes while sliding back to defend a low Arda Turan cross with Diego Costa lurking then on the strong of half-time Koke finished from a Costa ball into the box.
Ivan Rakitic also saw red late on, barely two minutes after Antonio Luna, a Sevilla sub, was sent away from the touchline by the ref.
And the job was completed in injury time when Turan pounced on a loose save from Andres Palop to set up a tap-in for Joao Miranda.
Barca later beat Levante, also by a 4-0 scoreline, to move three points ahead again.m