Matthew Thompson slotted home with the final kick of the game to earn another useful point for Worksop.
The squad was hit with absentees and illness before kick off, so the team had to be patched together.
However this was no excuse for the start SJR made, with a flat uninspired performance seeing them go 2-0 down early on.
Just before half-time they grabbed a lifeline when Scott Wesley headed home from a set piece.
After some honest words and a change of shape, SJR came out flying in the second half and were on the front foot from the off.
Cameron Baines (17) came on after an hour and his impact was immediate, driving with the ball, winning headers, and getting his foot in to help pin back Kiveton.
This seemed to inspire some of the older players and it was Tom Mullen who made it 2-2 with a fine strike.
Minutes later he was in again, after great work from Taylor Thackery, but his effort was saved well.
Kiveton then hit on the break to take a 3-2 lead.
With five minutes to go caution was thrown to the wind and SJR switched shape again to 3-3-4.
It paid off when Thompson hit a well struck shot into the top corner in the final seconds.
It was the eighth time this season SJR have come back from two goals down.
Elsewhere, SJR Under 7's put their narrow semi-final defeat last week behind them with an emphatic 11-1 victory and take third place in their cup competition.