The captain made it 2-0 to Gers in the first-half with an incredible, dipping effort from 25-yards which found the top corner, and it ensured Gers head back down the A9 this afternoon in fine fettle ahead of a huge week.
He also took time to praise the impact of Kemar Roofe who scored on his first start since April 2022.
Tavernier told RangersTV: "It was a quick interception, I was driving and I saw Kemar make a run to take the player away and my eyes lit up when I saw the goal. I am really happy it went in.
"Kem is a really good player for us - as is Tom Lawrence - and to have those two back in the squad fully fit is only going to make us stronger so I am delighted to see them back on the pitch today and Kem starting and getting his goal.
"We need all the players to chip in this season. It was really important to come here and get the three points.
"I was delighted we got the clean sheet and I thought the first-half performance, we were really dominant in possession and in the second half, we probably let them back into the game more than what we should have, but we kept a clean sheet and towards the end, Abdallah made an unbelievable header to keep it that way.
"So I am really pleased and it puts us in good stead for the PSV game."
On that PSV match, the captain added: "It is a big week ahead - we will look forward to the game at PSV - we know it is going to be a tough game but we are coming off the back of a win and a clean sheet so hopefully we can do the same over there."