With the Blues already confirmed as Group L winners, Maurizio Sarri made 10 changes to the side that beat Manchester City last weekend and was almost made to endure an embarrassing defeat.
The visitors made life difficult for themselves as an Ethan Ampadu own goal quickly erased Willian's 30th-minute opener, before Loic Nego fired the unheralded Hungarians into the lead 11 minutes after the restart.
But the loss of Alvaro Morata to a first-half knee problem proved an unlikely blessing in disguise for Chelsea as Giroud stroked in their second free-kick late in the match to ensure the Premier League side enter the knockout rounds unbeaten.
Vidi's deep defence made for a pedestrian start and it took Willian's moment of class to breathe life into the contest.
The Brazilian guided a fine free-kick beyond the cumbersome Adam Kovacsik, although the lead lasted less than two minutes as Ampadu awkwardly headed a corner into his own net at the other end.
10 – Since his Chelsea debut, Willian has scored 10 direct free kicks for the Blues – more than any other player. Precision. pic.twitter.com/nl6zVJuvkP— OptaJoe (@OptaJoe) December 13, 2018
Chelsea's luck continued to run against them when Morata, a largely peripheral figure, went down clutching his left knee in innocuous circumstances before the break and needed replacing.
The dangerous Nego left nothing to chance about the goal that put Vidi ahead, lashing home on the volley after Georgi Milanov spotted his run to the far post.
Giroud failed to capitalise on either of two good opportunities that initially came his way, but the France striker made amends in the 75th minute, mirroring Willian's earlier set-piece wizardry to seal a share of the points.
What does it mean? Sarri toys with momentum
So impressive in battling past Premier League champions City last Saturday, head coach Sarri might regret the wholesale changes he made for this trip.
The question of whether momentum has been squandered will be answered at the Amex Stadium on Sunday.
Nego bamboozles Blues
The brightest spark in an often lifeless first half, one-time Roma man Nego was full of enterprise in getting forward at every opportunity and his volley was a finish to savour.
Ampadu opens the door to defeat
Sarri has effectively told Gary Cahill he is free to leave the club in January and, though Ampadu's own goal is unlikely to be enough to make him reconsider that stance, it was an avoidable moment the teenager will be eager to forget.
Key Opta Facts
- Chelsea are unbeaten in their last nine Europa League games (W8 D1), last suffering defeat in the competition against Ruben Kazan in the second leg of the 2012/13 quarter-finals.
- Vidi are just the second side to score two goals against Chelsea in a Europa League game after Ruben Kazan back in April 2013.
- There were just 116 seconds between Willian's opener for Chelsea and Ethan Ampadu's own goal.
Chelsea will expect better when they visit Brighton and Hove Albion in the Premier League on Sunday, the same day as Vidi's home date with Hungarian leaders Ferencvaros.