The Blues needed to better Juventus’ result to finish top of their group.
It all started so well for Thomas Tuchel’s side as Timo Werner gave them the lead after just 90 seconds. It was the fastest goal they have ever scored in the competition.
But Chelsea failed to kick on and they actually went into the half-time break with a one-goal deficit.
Two goals in three minutes from Claudinho and Sardar Azmoun gave Zenit the lead.
But Chelsea battled back in the second half and it looked as if they would get the three points they desired.
Romelu Lukaku restored parity just after the hour-mark and Werner notched his second with five minutes remaining to give the away outfit the lead.
But they could not hold on as Magomed Ozdoyev scored a tremendous effort in the 94th minute.
The ball fell invitingly to the 29-year-old on the edge of the box and his sweetly-struck volley arrowed past Kepa and into the top corner.
It was a stunning effort and you can watch it below…
What a hit that is. Kepa really did not stand a chance.
That was Ozdoyev’s first goal of the season – and what a time to get it.
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Juventus beat Malmo 1-0 in Italy to finish top of the group.
Chelsea now face a very tough tie in the last-16. They could face Real Madrid or Bayern Munich in the first knockout round.
Tuchel’s side will find out their opponents for the next round when the draw takes place in Switzerland on Monday.