Boss Leese delighted as Kettering Town climb out of relegation zone
Second-half goals from Sam Bennett and substitute Tyrone Lewthwaite secured the three precious points for the Poppies, who moved out of the bottom four as a result, and up to 18th in the table.
It was only a second league win of the campaign for Leese's side, who have struggled to consistently find their best form.
Tuesday night was the team's first outing since they were beaten 5-0 at Vanarama National League leaders Chesterfield in the FA Cup final qualifying round, with last Saturday's scheduled date with leaders Mickleover being called off due to a waterlogged pitch.
But there was to be no hangover from that heavy loss to the Spireites or the enforced 10-day break as Kettering proved too good for Leiston.
The home side did have their moments and their chances, with Poppies goalkeeper Billy Johnson making some crucial saves, but once Bennett fired Kettering in front with 20 minutes remaining, there was only going to be one winner.
Lewthwaite then sealed the deal with a stoppage time second.
"I am delighted, I think it was probably our most rounded performance across the season," a very happy Leese told Kettering Town's YouTube channel.
"I thought we controlled the ball in possession really well in the first half, and we created more chances than we have been doing.
"Leiston had a spell after half-time where they caused us one or two problems, and Billy was called into action, but that is what he is there for.
"After that I thought we controlled it and saw the game out really well.
"There was some concern in the second half, I was a bit worried we weren't going to open them with all the good build-up play that we had.
"But I needn't have been concerned, because there was a great finish from Sam and equally good finish from Tyrone."
Kettering can now make further progress up the table on Saturday when they travel to Berkhamsted, knowing three points will see them leapfrog Leiston one place above them on goal difference.