It is a two-horse race for the title, with third-placed Valencia 16 points behind with a game in hand, but Real now hold the edge.
Barca's trip to the Bernabeu on the April 10-11 weekend could be the key, with the head-to-head record between the teams deciding the title if they finish level on points, as happened in 2007.
Barca beat Real 1-0 in the Nou Camp earlier this season.
Sevilla, one of only three teams to have beaten Real this season in the league, went two up at the Bernabeu but were swept aside as Real scored through Cristiano Ronaldo, Sergio Ramos and finally Rafael van der Vaart.
"The key for me was that this Madrid were able to play the kind of electric football they are capable of," Sevilla coach Manolo Jimenez told reporters.
"I have to say that this Madrid is electric, with power and speed, incredible. It was very difficult to keep Madrid away from our goal, given how fast they are."
Real midfielder Xabi Alonso said the win was a huge boost to morale ahead of Wednesday's visit of Olympique Lyon in the Champions League, when they have to overturn a 1-0 first-leg deficit.
CONFIDENCE BOOST
"We have played as a team and everything worked well," he said. "This gives us a lot of confidence in the league and for Wednesday's match."
"There's still a long way to go (in the league) and a lot of things can happen, but we are moving in the right direction."
In contrast, Barcelona's faltering form cost them dearly when they were held 2-2 in Almeria, having to twice come from behind to level through Lionel Messi.
The pressure on the leaders appeared to be reflected in Pep Guardiola's being sent to the stands in the first half and then striker Zlatan Ibrahimovic saw red in the 61st minute.
"Despite the sendings off, and the adverse result, we didn't lose faith," Guardiola told reporters. "We continued to press forward with 10 men and for this reason I am proud of the players."
When asked about his sending off, Guardiola was brief in his reply. "Ask the referee," he said. He was clearly annoyed when asked whether he was feeling the strain, saying: "No. I'm not tense."
