The Roosters headed into Saturday's contest having lost four of their opening five matches of the campaign and stuck in the bottom two.
But, the combination of their highest score of the season to date and some superb bowling by paceman Jonny MacGregor ensured that the visitors' challenge was brushed aside.
Harry Allinson (58) hit a half-century at the top of the order before Ben Moss (66) and Ben Kempley (62) followed suit, the latter pairing sharing a stand of 112 as 'Gate were all out for 260.
MacGregor then helped himself to 6-22 as Acomb were skittled with just 96 on the board, fellow quick bowler Mat Pillans also doing his bit by grabbing 2-20.
Second-from-bottom Sessay were beaten in dramatic fashion at home to Scarborough.
Having won the toss and elected to bat first the hosts put 241/8 on the board, Nasir Jamal (100) smashing a stunning quick-fire century from only 64 deliveries.
Skipper Mark Jackson (56) and Mark Wilkie (47) also contributed to leave the Thirsk outfit in a strong position at the halfway stage of the contest.
A 152-run first-wicket partnership got the seasiders' reply off to a fine start before wickets began to fall, Ben Kettlewell taking a couple of scalps.
Then, with the scores tied ahead of the final delivery of the Scarborough innings, Breidyn Schaper (59 not out) hit a six to move his team onto 247/8, condemning Sessay to a cruel defeat.
In Division One West, Harrogate 2nds got the better of Studley Royal away from home.
Charlie Stokes (48 not out) and Ash Griffin (47) led the way for the Roosters as they made it to 202, Matthew Coad bagging 4-25 and Dan Craven 3-59.
Craven hit 39 in response and Dan Coad chipped in with 32, however that was as good as it got for the home side, who were sent on their way with the scoreboard reading 142.
Stokes completed a superb afternoon's work by scooping 4-27 with the ball, helping 'Gate up to third in the table, where they sit just behind Knaresborough.
Greg Pickles' men returned to winning ways following their first loss of the campaign last time out, chasing down South Milford's total of 247 all out.
Tashmial Henry knocked over four of the home batsmen, then went on to top-score with a knock of 52 as Knaresborough completed a five-wicket triumph in the 38th over.
Howard Johnson struck 45 and opener Kevin Owens also looked in decent touch, making 42.
Thirsk remain top of the pile with 60 points from a possible 60 after struggling Dringhouses conceded Saturday's fixture.
Ferdinand Rex plundered a century as Sessay 2nds went big when they visited rock-bottom York 3rds.
He weighed in with 113 of the visitors' 340/7, Rory Hall hitting (54 not out) and James Skelton (44) while the home attack gifted away 48 runs in wide deliveries.
Cameron Luck then affected a trio of dismissals to help ensure that the basement boys didn't progress any further than 218/9.
In Division Two Galtres, Pannal slipped from second position to third as a result of their agonising one-run reverse at Rufforth.
The hosts posted 257/5 from their 45 overs and a fine unbeaten ton from opener Rob Ellis ensured that the men from Burn Bridge Lane were always in the hunt when they took their turn at the crease.
His knock of 119 came from just 125 balls and featured 10 fours and three sixes, while Matthew Firbank (45), Martyn Wood (38) and Rob Smith (36) all did their bit.
The match went right down to the wire, though Pannal eventually ended up one run short on 256/5.
Rob Taylor was another player to hit a century in vain, the Ripon opener smacking 120 of the hosts’ 208 all out against Duncombe Park.
Andrew Lincoln contributed 36 to an excellent opening partnership of 123, though it was pretty much all downhill from there for the home team.
Jake Briscombe managed to grab a couple of wickets when Park replied, but the visitors cruised to 210/4 with more than eight overs in hand.
Second-from-bottom Knaresborough 2nds secured their maiden victory of the summer, overcoming Malton & Old Malton 2nds.
Ben Ward (84) and skipper Graham Dodds (46) impressed with the bat in an innings of 248/8.
A haul of 5-44 from Tom Wilson then helped get rid of Malton for 202 in the 44th over of their reply.