The bonus-point victory was the Lily Hill men's first triumph for over a month, and comes on a weekend when nearest rivals Westcliff, London Irish Amateur and Staines
While the five points for the win are undoubtedly priceless in Bracknell's fight for survival, so too was the impressive performance, which Leishman hopes his side can repeat in the coming weeks.
"We had been threatening to put in a display like that for a while and I thought that we played well," he told the News.
"Hopefully we can play as well as we did on Saturday every week. We know we need to get a run going and we are under no illusions that we are still in trouble, but things are certainly looking better now."
Indeed, with matches coming up against Staines this Saturday (2.15pm ko) followed by London Irish Amateur and Westcliff, March could be a decisive month for Bracknell.
They currently sit seven points adrift of safety and Leishman believes they can close that gap in the next few weeks.
"There's just a bit more belief around the team now," he commented. "We know that we still probably need to win all of our games and that there's still a long way to go, but we have edged a bit closer to safety."
Leishman's side fell behind on Saturday to an early Tom Newton penalty but fought back well to come out on top.
Ian Higgins scored the hosts' first try on 10 minutes before Ian Burch burst clear for a touchdown that Ben Nowak converted.
Nowak was on hand again to kick the extras from Charlie Davy's breakaway try as Bracknell established a 19-3 advantage.
Although Tring enjoyed nearly as much possession as the home side, they were unable to break through the defensive line to add to their score.
And Bracknell secured the bonus-point victory when Stuart Mackay and replacement Nico Maybury - who has returned to the club after a spell travelling - both touched down.
Another replacement, Chris Brember, put the icing on the cake when he scored with his first touch of the match and Nowak completed the emphatic triumph with the conversion.