Perbet fired home in the fifth minute as the visitors ended a run of four matches without a win to reignite their faltering push for the European berths.
The 1-0 reverse leaves Getafe coach Cosmin Contra still searching for his first win since taking charge a fortnight ago.
After opening his tenure with an entertaining 3-3 draw with Granada, Thursday's loss was a second in succession for the new man - having gone down 1-0 to Athletic Bilbao at the weekend - and leaves the club still mired in the bottom three.
The fans at the Coliseum Alfonso Perez dearly hope Contra is the man who can guide the club to a first win in La Liga since the end of November, yet they had barely settled in their seats before what would prove to be the match-winner was nestling in the Getafe net.
Bojan Jokic was involved as he found Perbet just inside the area, the French striker showing all the confidence of a fine season as turned and fired powerfully beyond Jordi Codina at his near post for his ninth league goal of the campaign.
Perbet might have doubled his tally on 21 minutes but Codina blocked his effort before Oliver Torres drilled wide on the rebound.
Getafe's response to falling behind was conspicuous by its absence, with Adrian Colunga's close-range effort, which forced Sergio Asenjo into a routine save, their only threatening moment before the break.
The hosts pushed on a little more after the interval as Villarreal sat back to defend their advantage, but chances remained thin on the ground with Pedro Leon and Lisandro Lopez both wasteful with the pick of what openings they carved out.