Bourne need 20 points from their final two games to lift the Lincolnshire Premier League championship.
Despite managing only a losing draw at title contenders Bracebridge Heath, the leaders picked up sufficient points to stay well ahead of their two main rivals.
Bracebridge notched up 252, losing their final wicket on the last ball of the innings, with Hymie Bentley contributing 53 and Carl Stubbs 68.
They shared a stand of 77 after the home side had been reduced to 95-5 and Stubbs put on a further 52 with Matt Carter before falling to Ben Stroud who claimed four wickets.
Bourne suffered a similar fate, losing their first three wickets for 45 runs, but an outstanding display of batting from Conrad Louth – who had taken four catches in the first innings – brought a partnership of 128 with Carl Wilson (69).
Louth eventually fell to Carter for 106 and the innings closed on 227 -7, giving Bourne 13 points.
The foot of the table provided Saturday’s surprise results with Market Rasen recording their first victory to move off the bottom.
Spalding were Rasen’s victims, succumbing for just 96 as Tom Borysczuk claimed six wickets for 22. Graeme Bell then got among the runs with 55 to start the celebrations of a seven-wicket victory.
Billingborough, who were between Grimsby and Rasen in the table, had less success at Market Deeping where Chris Jones hit 87 to help his side to 182-9 at the close.
Billingborough then came up against an in-form Tom Andrews who bowled his full 17 overs, giving away just 18 runs and taking five wickets as the visitors were bowled out for 85.
Billingborough and Market Rasen are now on equal points, with Rasen in 11th on the number of victories.