With youngster Isaac Light in fine form at the top of the order, the Roosters put 229/9 on the board in 50 overs after winning the toss and elected to bat first.
Light led the way with a quick-fire knock of 79, Ben Moss adding a useful 38 at number six.
But, although Ed Booth, Mat Pillans and Ishan Abeysekara each bagged a couple of wickets to keep ‘Gate very much in the contest, Grange eventually reached 232/7 in the game’s penultimate over.
Defeat sees the men from St George’s Road drop one place to ninth in the table, having been leapfrogged by local rivals Sessay.
Mark Wilkie's side bowled Sheriff Hutton Bridge out for 174 and chased that target down with relative ease.
Nasir Jamal (3-39) and Stephen Langstaff (3-45) were the pick of the away attack, while the former also shone with the bat.
Having smashed a century against Scarborough last time out, the Afghanistan international finished unbeaten on 74, while Jacob Spencer contributed an important knock of 50.
The pair's efforts saw Sessay reach their victory target with five wickets and four overs in hand.
Harrogate 2nds were soundly beaten by Division One West leaders Thirsk, who extended their 100 per cent start to the season into a seventh match.
Cooper Smith (34) was the only 'Gate batsman to make any real impression in a first-innings total of 126, Stuart Christon (6-30) wreaking havoc for the high-flyers.
Harry Collinson then struck 40 as Thirsk made light work of their run-chase, cruising to 127/4 inside 21 overs.
Defeat leaves Harrogate's second string fourth in the table.
Second-placed Knaresborough made it six wins in seven to keep up the pressure on Thirsk when they entertained Sheriff Hutton Bridge 2nds.
Toby Giddings hit 72 not out as the home side made their way to 238/7 after 50 overs.
Bridge's reply never really got going and they were reduced to 70/6 before finally being knocked over for 140, Jordan Tear impressing with a haul of 4-20.
Third-placed Studley Royal beat Heworth by 44 runs.
Jonny Harding (68) and Dan Coad (42) top-scored as the Ripon outfit were all out on 218.
Nicholas Cunningham then took 3-24 as the hosts were sent on their way with the scoreboard reading 174.
Sessay 2nds lost out by a six-wicket margin at home to South Milford.
Joseph Watson (40), Stuart Clark (39) and James Skelton (36) all chipped in with the bat, helping their team to 183.
James Easton claimed a couple of scalps when Milford responded, though the away team had no problems whatsoever in knocking off the required runs.
In Division Two Galtres, Pannal kept pace with the promotion places courtesy of a 14-run triumph over Acomb 2nds in what was a high-scoring affair.
Andy Ellis (150 not out) and skipper Rob Ellis (127 not out) both went big for the men from Burn Bridge Lane, smashing 28 fours and no fewer than 14 sixes between them in a total of 310/1.
But, despite having seemingly been left with a mountain to climb, Acomb made a good first of their reply, battling to 296/8.
Moses John was the pick of the Pannal attack, finishing the afternoon with a trio of dismissals under his belt.
Ripon slipped into the bottom-two after they were turned over by basement boys Malton & Old Malton 2nds.
Opener Rob Taylor (76) was once again the only home batsman to really impress, making more than half of his side's 141 all out.
Jake Briscombe then helped himself to 3-23, however his efforts weren't sufficient to prevent the visitors from reaching 142/6.
Knaresborough 2nds escaped the drop-zone thanks to a narrow success on the road at Osbaldwick.
David Artindale (56), Oliver Ward (51), Ben Ward (45) and Andrew Ward (37) all shone with the bat for the visitors, guiding them to 221/5.
A fine display of bowling from Jack Lowther (5-43) then helped restrict Osbaldwick to 210/8.