The match points were slipping away until the rink of Linda Cave, Ron Blake, Rose March and Neil Crees suddenly got the measure of the home surface and racked up 14 shots in the last seven ends.
It was enough to turn the tide and they ran out 30-17 winners.
Elsewhere the rink skipped by Dennis Henshaw forced a draw on the last end to help claim the points 9-5 in an overall 77-69 victory.
Lincs Mixed league: Grantham 69 (5 pts) Stamford 77 (9). M Smith, J and S Suffling, D Henshaw drew 14-14; L Cave, R Blake, R March, N Crees won 30-17; M Ramsden, S Henshaw, S Moir, J Hare lost 15-16; R Roberts, J Lonslow, A March, D Cave lost 18-22.
Following defeat in their opening League match Stamford Over 60s recovered to take 12 points from Southern Division newcomers Lincoln B in an 81-52 win.
Rink honours went to Pete Linnell, Peter Smith, Charlie Jones and Martin Hewitt with a 26-8 win over 21 ends.
Lincs Over 60s (South): Stamford 81 (12) Lincoln B 52 (2). Stamford names only: I Hall, P Shaw, D Oakey, T Scarr lost 10-19; T Barwell, A Hynes, D Henshaw, B Warters won 24-17; P Linnell, P Smith, C Jones, M Hewitt won 26-8; J Bourne, S Miner, P Burt, J Holroyd won 21-8.
For the first time in several years, Stamford competes in the national Top Club competition on Sunday (10 am) which features mixed singles, pairs, triples and fours.
The match at Grantham on October 27 (10 am) will be captained by new member Tom Newman-Borrett.
The team to visit Grantham is: singles Yvonne Monaghan & Martyn Dolby, pairs Michelle Smith and Tom Newman-Borret; triples Rita Downs, Mick Humphreys, Jon Earl; fours Elizabeth Wallace, Chris Ford, Neil Wright & Adam Warrington.