With temperatures in the high 20's the teams, who had similar records in the league set out with a win in mind, but it was Bedford, playing uphill in the first half that began to get the better chances.
Tomlinson, Ben Ford and Dan Walker were amongst those who came close to scoring for the visitors, but it was Callum Milne who would break the deadlock in the last seconds of the first half.
He entered the area, and despite having two team mates available, he took the ball on and slotted it into the bottom left hand corner in what was to be the last action of the half.
The early stages of the second half saw more chances for Walker, with a shot hitting the post, and another going just wide of the left-hand post.
North Leigh never looked like coming back once the Eagles got their second. A corner came over and was cleared to Callum Donnelly, 25 yards out. His shot was true but the ball deflected off Joe Steeles head, wrong footed the keeper and droped into the net.
With Bedford in control the joint managers made changes, bringing on Nathan Olukamni, Ebby Nelson-Addy and Jack Vasey for his first outing this campaign.
Olukanmi in particular put the home team under pressure, he took the ball down the left from inside his own half, and got to the left corner of the area, after leaving at least four players in his wake. He got a shot off, but it was saved.
Walker, who was unlucky not to score earlier, continued the trend, this time hitting the right hand post.
The win saw Bedford climb three places to eighth in the table.