Lima scored twice to help Benfica to a 4-0 victory at home Penafiel, condemning their visitors to relegation on Saturday.
The Brazilian striker netted in each half as Benfica made it six league games without defeat, while moving six points clear of rivals Porto, who face lowly Gil Vicente on Sunday.
But it will be second-tier football next season for Penafiel, who needed to take something from the match to keep their slim survival hopes alive.
Lima opened the scoring in emphatic fashion after eight minutes at Estadio da Luz, running onto Maximiliano Pereira's cross and heading powerfully past Alireza Haghighi.
Fellow Brazilian Jonas doubled the home side's lead on the half-hour mark, with a composed finish from just inside the area after being played in by Eduardo Salvio.
Pizzi curled a low shot into the bottom corner of the net in the 60th minute, before Lima pounced on a poor back pass to round the goalkeeper and complete the scoring two minutes later.
Maritimo were the only other team to win on Saturday, accounting for fourth-placed Sporting Braga 3-1.
The scores were level at the break, but second-half goals from Danilo Pereira and Moussa Marega helped Braga end a run of three consecutive draws.
Elsewhere, Fabio Nunes equalised in the 90th minute as Belenenses salvaged a 1-1 draw at Academica, while Rio Ave and Pacos de Ferreira ended goalless.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.