The county men looked to be heading for defeat in the third period on Sunday night, despite scoring first, after Swindon took the lead with two quick goals during the second session.
But a late equaliser and then that winning strike from Sam Zajac in overtime secured Telford's second successive home win.
Watkins, who watched his side deliver a remarkable 49 shots on goal, was delighted with that dramatic late effort.
He said: "I said to the guys that I thought we played well for the whole match and put in solid performances all over the ice.
"The other side are bound to get a few goals, but we stuck to what we had to do. We kept putting pucks in on the net, kept battling down low and created a lot of scoring chances.
"The big thing for me is that we didn't lose our belief. We had a couple of powerplays, and perhaps we weren't as crisp as we'd like to be. But the guys kept doing it and Pete (Szabo) popped in to steal a goal and tie it up."
A tense encounter saw the English Premier League champions draw first blood on 21 minutes, thanks to captain Jason Silverthorn. The visitors drew level seven minutes later, before taking the lead at the halfway point of the game. The match appeared to be drifting towards another loss for Telford, until Szabo struck with just three minutes left.
That goal sparked a tense period of overtime, with Sam Zajac netting the winner just a few minutes later.
Watkins added: "Three on three is great to watch, although it's easy to say that when you've just won. But we created a lot of chances and it was like a game of ping pong, going back and forth.
"Sam Zajac played the last five minutes of the third period and the first two minutes of overtime. It was a great effort and Sam showed some great leadership tonight."
The Tigers hit the road at the weekend, going to Swindon on Saturday and Peterborough the following day. Next home game is October 25 against Milton Keynes.
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