Salvi's early spot-kick and a neat finish from Cervi shortly after the interval were enough to hand Kyiv the three points to boost their Group B qualification hopes.
Second-half heroics from Benfica's Ederson protected its advantage as Kyiv fought for a route back into the match, the goalkeeper saving expertly from Junior Moraes and Andriy Yarmolenko.
It was a textbook away performance from the Portuguese champion, happy to concede possession to its hosts and defend resolutely before hitting on the counter.
Serhiy Rebrov's men have now won just two of their last nine games in all competitions and prop up the group with just one point, ahead of the reverse fixture between the two clubs in Lisbon next month.
Benfica tore out of the blocks and into its host, and was rewarded as early as the ninth minute when referee David Fernandez Borbalan pointed to the spot after Vitorino Antunes clipped the heel of Goncalo Guedes as he skipped into the penalty area.
Salvio stepped up and sent Artur Rudko the wrong way, slotting calmly to the goalkeeper's left for his second goal in as many Champions League games.
Kyiv's talismanic captain Yarmolenko almost dragged them level, first picking out fellow winger Derlis Gonzalez at the far post to head over, then teeing up Serhiy Sydorchuk five minutes before the interval to fire into the side netting.
The visitor was a constant danger on the break and Salvio could have doubled his tally from a quick Benfica counter, but shot too close to Rudko.
Salvio turned provider for Benfica's second in the 54th minute, squaring for Cervi after a darting run down the right flank.
Cervi saw his first effort blocked, before composing himself and wrong-footing Rudko with a sweet finish.
Kyiv responded positively and the visitor had goalkeeper Ederson to thank for a string of impressive saves to protect its two-goal advantage.
First he came out quickly to smother Moraes' shot as he raced free in the box, before a superb double save after 66 minutes from Yarmolenko and Sydorchuk as the host pushed for a way back into the contest.
He almost blotted his copy book just moments before, racing out to try to punch clear a cross and missing completely, but a surprised Yarmolenko could not direct his header goalwards.
Yarmolenko really should have grabbed a consolation in the dying stages as he attempted to acrobatically convert a rebound, but Victor Lindelof somehow blocked his effort to preserve his side's clean sheet.