Two early solo efforts from striker Ellie-Mae Bloomfield placed the home side in the ascendancy, a lead that they maintained until the half-time interval, RI going close with a couple of long-range efforts.
After the interval the York side stepped up a gear but Bloomfield completed her hat-trick with a penalty-kick and the three points looked set to be heading to Scarborough.
RI refused to give in, though, and struck twice in quick succession. The home side twice went close to adding a fourth to secure the win, but in the closing moments York earned a point.
Bloomfield was named as the lady of the match for Scarborough, but for the second week running it was a superb all-round effort from an improving team.
The Under-14s head to Wigginton on Saturday.
Scarborough Ladies Under-13s hosted Brayton Belles at a sun-drenched Sherburn and came out resounding 10-3 winners.
Boro blasted into a 6-1 half-time lead in the City of York Girls League game with goals from Alesha Grime (2), Rebecca Addison (2), Lola Bayes and Gracie McLoughlin.
Brayton fought back in the second half with a couple of goals, but the home team were always too strong and added another four with both Grime and Addison completing their hat-tricks and a further strike apiece from Bayes and McLoughlin.
A special word of praise goes to Kayla Brook, who donned the goalkeeper gloves at short notice and saved a penalty late in the game.
Scarborough Ladies Under-12s claimed a superb 2-1 win at title-holders Bishopthorpe.
The hosts started the strongest of the two teams with two early efforts to no avail.
These attempts were well defended by debutant Ruby Isherwood.
Then Scarborough started to get a foothold into the game when a shot from Lily Mae Bayes was saved.
Scarborough continued the pressure, carving out some great chances without any joy, while Bishopthorpe tried hard but were not good enough to make an impact in the game.
But then the chance broke for debutant Pippa Wedge, who put the ball through to Alice Wood, who slotted home to hands the Reds the lead heading into break.
The Reds came out slowly in the second half and conceded a well-worked goal from Bishopthorpe.
That was the wake-up call the Reds needed.
Rachel Hodgson had a few chances with one from the half-way line going narrowly wide.
Then the Reds broke free and Harmarni Winn Atkins was taken down, winning a free-kick.
Up stepped Hodgson, who drilled home into the top corner with a superb finish.
The Reds finished 2-1 winners and play Wigginton at home on Saturday.
Girl of the game went to Winn Atkins who gave 100 per cent for the team.
Scarborough Ladies Under-15s picked up their first point of the season in an entertaining 5-5 draw at Poppleton Tigers.
Dominating from the kick-off, Scarborough raced into a 2-0 lead in the first five minutes with well taken goals from Amelia Breckon and Lucy Fairbank.
However, Scarborough’s frantic pace couldn’t be maintained in very warm conditions and Poppleton got back into the game with two goals to go into half-time 2-2.
Poppleton started the second half on top with two long range goals to lead 4-2.
This seemed to wake Scarborough up who then played some great attacking football and hit a further three goals, Fairbank netting her second of the match and Kelsey McGough scoring two to lead 5-4.
A breakaway equalising goal in the dying minutes from Poppleton then took the score to 5-5 and overall a fair result.
Scarborough’s player of the match was Sophie Smith.