Prior to the game, the two promotion rivals were separated by three points but the Tudors moved level with their opponents after a superb team display.
And boss Steve Bateman revealed his delight at the efforts of his charges.
"Normally I tell the players that we need at least eight of them to hit top form if we're to win games but on Saturday, all 11 of them were superb," he beamed.
"We're in a situation at the moment where we can't afford to slip up.
"Whether that's focused everyone's minds or we've just run into a rich vein of form, I don't mind which because the outcome is that we picked up another win.
"Not only did we play well but I was chatting to their manager afterwards that no-one had ripped them apart like that this season and if we'd been seven or eight up by the time they'd got back into it he wouldn't have argued at all."
Bashley have a great home record this season but the Tudors played like men possessed, outclassing their opponents at times.
Skipper Paul Edgeworth had headed the visitors into the lead before Dillon, who is on fire at the moment, added a second just before the half time interval.
And just two minutes into the second half, Dillon set up strike partner Cooper to put the game beyond the reach of the hosts.
Although the Tudors took their eyes off the ball somewhat, allowing Bashley to pull two goals back, boss Bateman was always confident the points would be going back to Vauxhall Road.
"Even when we started letting them back into the game, I always knew that we were more than capable of going back up the other end and scoring a fourth or a fifth if necessary," he said.
"We seemed to be able to open them up at will and it was very pleasing to see both our strikers on the scoresheet again."
The seemingly intuitive partnership that Dillon and Cooper have struck up since the latter joined the club has certainly reinvigorated the Tudors and re-ignited their title challenge.
And Bateman believes that Saturday's visitors to Vauxhall Road, Chippenham may be wary of the deadly duo.
"Chippenham won't relish coming to us," he said.
"They know we're capable of scoring goals, create things out of nothing and that we're in a rich vein of form at the moment.
"If we beat them on Saturday, we'll only be two points behind them so perhaps they are a more realistic target for us than Bashley.
"There's a lot to play for but the important thing is to concentrate on what we're doing and go out and get another three points.
"The support, both home and away has been fantastic but we'd love to see even more through the gates on Saturday because this game is huge for us and the extra support would be great."