Silva is currently sidelined with injury but watched on in excitement as his team-mates secured a 3-0 aggregate win over the La Liga leaders.
Goals from Hakim Ziyech and Emerson Palmieri secured the victory on the night, with Thomas Tuchel maintaining his unbeaten record since taking charge of the club.
As Emerson’s strike hit the back of the net, top cheerleader Thiago went wild.
He rushed up the Stamford Bridge steps to hug team-mates Mason Mount and Jorginho – who missed the match through suspension.
During the match, Thiago was seen stood in the middle of the stands screaming out instructions to team-mates.
It seemed to do the trick as they put in a controlled display against a formidably European opponent.
Goalscorer Ziyech was delighted with his side’s win. He told BT Sport: ‘Some difficult moments in the game but for most of the time we had it under control. It was an important goal and I had to wait a long time for it.
‘It is always good when you go 1-0 up, especially when you make it by yourself. Timo’s delivery was good as well.
‘It was a bit like seeing how the game would go for 10 minutes and after that we had control. We did well.
‘They didn’t create a lot. We can be happy about the performance. Hopefully it will be a good opponent for the last eight.’