Jack White impressed on his List A debut before heavy rain prevented the visitors from chasing 223 and forced a Royal London Cup No Result at Scarborough.
Yorkshire were bowled out in the 50th over from being six down for just 69 in the 21st having been invited to bat in overcast conditions.
Northamptonshire took advantage superbly, led by new ball seamer Jack White with three of the first four wickets to fall on his List A debut. But Luxton’s intervention took valuable time out of a game which saw only five balls of the chase bowled and no play beyond 3.05pm.
The visitors needed to face 10 overs to avoid a one-point apiece No Result, with a revised target of 73.
And had Luxton been given out on five when the Steelbacks felt they had him caught behind off the spin of Graeme White, there is every chance they would have got that chance to claim victory.
Instead, Yorkshire’s Academy captain took advantage to hit five fours and two sixes, both down the ground, in an impressive 85-ball knock.
Having reached a 72-ball fifty, he received a standing ovation from a 2,000 strong Scarborough crowd when bowled by Wayne Parnell to leave the score at 214 for eight in the 48th over.
Like Jack White, Taylor also claimed three wickets, though conceded 64 in 10 overs.
White, 29-years-old and having only played five previous first-class games was the standout bowler with three for 38 from his 10, eight were bowled in his opening spell.
Having consistently moved the ball away, he bowled Harry Duke with one back in through the gate, leaving the score at seven for one in the third over.
George Hill was then brilliantly caught and bowled pushing at one and Will Fraine, for 28, caught at deep square-leg pulling.
Despite restarting unaffected, rain arrived just 5 balls into the Northamptonshire innings and took the players from the field. A 5.50pm restart was teased after rain stopped, but the outfield was too wet and the teams bumped fists shortly after 5:30pm.
The Steelbacks now travel to London to take on Surrey on Friday before returning to The County Ground on Sunday.
Tickets for the three remaining Royal London Cup fixtures at The County Ground, plus the final two fixtures of the LV= Insurance County Championship are now available to order online.