The Whites claimed their third win to move them up to third place in the early league standings with a 2-1 win over newly promoted Halifax - watch match highlights here.
After narrowly missing out on the play-offs last season, manager Chris Kinnear rebuilt his side this summer and they've already hit the ground running.
An opening day win at Hartlepool United was followed by a home defeat to Kent rivals Bromley. Dover bounced back, though, beating Wrexham at Crabble before winning at the Shay on Tuesday.
Mitch Brundle put Dover ahead in the 87th minute but Tom Denton equalised for the hosts in the 91st minute - their first National League goal.
But deep into injury time Sho-Silva pounced to score his first goal and hand Dover the points, he said: "I'm buzzing! The boys put in a shift for the whole game. It was unfortunate that they scored but it was good to get the winner and the three points away from home.
"Connor won the header and the keeper parried it into my path, and I just had to put it in. If I get a chance I just have try and put it in the back of the net so I'm happy I'm off the mark now and we can kick on to Saturday."