Benzema produced two clinical finishes inside the opening 30 minutes to put Madrid 2-0 up at Balaidos, although Santi Mina pulled one back for the hosts against the run of play before half-time.
Despite plenty of pressure from Eduardo Coudet's side in the second half, Madrid held firm and secured the victory late on through Marco Asensio to extend their unbeaten LaLiga away run to 10 games – the first time they have achieved this since May 2016 when they went 11 without defeat on the road.
The result moved Zinedine Zidane's men above Barcelona into second, three points behind Atleti, but Diego Simeone's men can restore the six-point advantage over their neighbors if they overcome Deportivo Alaves on Sunday.
Madrid went ahead with their first shot on target in the 20th minute, Benzema superbly steering into Ivan Villar's bottom-left corner after a neat turn and pass from Toni Kroos.
Vinicius Junior then inexplicably chested over from four yards with the goal at his mercy, but his blushes were spared on the half-hour mark when Benzema grabbed his second.
Kroos was again the provider, the German picking Renato Tapia's pocket on the edge of the area and feeding Benzema, who slotted past Villar for his 17th LaLiga goal of the season.
Celta clawed their way back into the game five minutes before the interval when an unmarked Mina headed beyond Thibaut Courtois from Denis Suarez's free-kick.
Courtois had to be alert shortly after the hour mark to repel Iago Aspas' effort from distance as Celta pushed forward in search of a leveller.
Aspas then struck the post with a deflected free-kick inside the final 10 minutes but it was Madrid who had the final say, substitute Asensio guiding Benzema's cross home deep into stoppage time.