Primeira Liga Wrap: Benfica ease to win
Last year's runners-up headed into the encounter holding a four-point lead over Sporting Lisbon with a game in hand.
And they comfortably stretched their advantage to seven points courtesy of Lima's first-half double and a further goal from Enzo Perez in the second period.
Champions Porto kept up the pressure on Sporting, yet made hard work of beating Belenenses 1-0.
Any hopes the underdogs had of emerging victorious appeared to have extinguished when Joao Afonso was sent off in just the 44th minute.
However, the strugglers battled valiantly and it was not until the 79th minute when the decisive goal came as substitute Juan Quintero earned the points.
The victory leaves Porto five points behind Sporting, who occupy the final UEFA Champions League spot, while Belenenses fell to the foot of the table.
Pacos enhanced their chances of avoiding relegation with a 3-1 victory over fellow strugglers Arouca.
Jorge Costa's side began the day just two points ahead of the relegation play-off zone.
However, they increased that gap as Bebe's double complemented Yonathan Del Valle's opener to overshadow David Simao's penalty.
In the day's other game, Federico Dionisi's penalty cancelled out Mario Rondon's goal as Olhanense and Nacional played out a 1-1 draw which moved the former off the bottom of the table.