A stunning run and finish from Tendai Chitiza had got the Daniels back on level terms after Mark Jones' early opener for Sports.
Centre-half James Blunden then rose highest to head home the winner with 15 minutes of the contest remaining.
Stamford manager Graham Drury had a virtually full-strength squad available - with the exception of James Hicks - for the visit of their Southern League Premier Division Central neighbours.
However, it took the higher level visitors less than a minute to open the scoring through Mark Jones.
Sports' trialist had forced a corner off Jordon Cooke and, from Lewis Hilliard's inswinging delivery, Jones bundled home from close range.
Dan Haystead then had to be alert to palm away a stinging shot from Dan Jarvis before closing down Sports' trialist to block his goalbound effort.
Stamford created two good chances to level as first Cosmos Matwasa and Tendai Chitiza combined for the latter to clip a cross to the back post where the incoming Connor Bartle saw his effort brilliantly blocked by Lewis Moat in the Sports goal.
Moat then thwarted Harry Limb from close range with the Stamford striker just failing to get a strong enough connection on Tom Siddons' centre to beat the Sports custodian.
Sports came close to doubling their lead on the half-hour mark when Jones met a cracking cross from Jarvis at the back post only to see his header fly over the crossbar.
Siddons was the next Stamford player to be denied by the rapid reactions of Moat who got the slightest of touches on his first-time shot to divert it over the crossbar to ensure Sports held their one-goal lead at the break.
Moat continued to keep Stamford at bay at the start of the second half with another top stop to thwart Chitiza after Matwasa's deft pass had sent his team-mate free.
The Daniels were the dominant force during the early exchanges of the second period with Siddons and Rob Morgan also going close.
They were finally rewarded just before the hour mark with a top drawer effort from Chitiza.
Chitiza cut in from the left and after, beating his man, unleashed an unstoppable strike into the top corner of the Sports net.
This stung Sports back into life and Josh McCammon caused concern in the home defence with a lively burst before Cooke needed to make a last-ditch tackle to deny Cameron Johnson.
Both sides then made a flurry of changes as the game entered the final 20 minutes and it was Stamford who seized the advantage.
Jack McGovern's floated corner to the back post was met by the rising Blunden whose header looped over Moat and into the net with 15 minutes remaining.
Jack Duffy then went close with a header from Joe Burgess' cross before a couple of late Sports raids were repelled by the Daniels rearguard to ensure the victory.