The 97-run victory moved them within a point of fourth-placed Scothern and 52 points behind leaders Scunthorpe Town.
Alkborough won the toss and elected to field on a beautiful afternoon, but it was Rasen who started stronger as openers Dave Papworth and Will Bradford scored freely in the first 10 overs.
Bradford departed shortly after the pair had put on 50 for the first wicket.
But despite losing another wicket, Rasen continued to dominate as they went past the 100 mark approaching the drinks break.
George Fussey had joined Papworth at the crease and the pair were looking good until Papworth was bowled only one run short of his half-century.
When Matt Rutherford joined Fussey at the crease, Rasen looked to be heading towards a big total, but despite 39 from Fussey and 27 from Rutherford the second half of the innings belonged to the home side.
Rasen lost eight wickets for just 50 runs as the visitors were bowled out for 180.
Pick of the bowlers for Alkborough was Andy Williamson with 4 for 21.
In reply, Rasen signalled their intent from the start as they piled on the pressure with some impressive bowling.
Bradford ran in and bowled superbly as he destroyed Alkborough’s top order, and after six overs, Alkborough were 9-4 and in all kinds of trouble.
Bradford continued to bowl brilliantly, taking 5 for 8 in eight overs, and was well backed up by Liam Entwistle and Rutherford as Alkborough were struggling on 21-6 after 15 overs.
Despite a defiant stand from the lower order, Rutherford was able to carry on from where he left off seven days earlier.
The former county player took 4 for 17 as Alkborough were bowled out for 81, leaving Rasen to claim a 20-point haul.
Rasen: D. Papworth 49, W. Bradford 22, L. Chambers 4, G. Fussey 39, M. Rutherford 27, G. Bell 14, R. Chamberlain 0, D. Christie 0, C. Scales 11, L. Entwhistle 0, M. Bedford 4*, Extras 10. Total: 180.
Bowling: W. Bradford 8-3-7-5; L. Entwhistle 7-0-29-1; C. Scales 6-0-26-0; M. Rutherford 5.2-0-17-4.