Greenwood and Garbutt made light of the event being reduced to 16 holes due to the seventh and eighth holes being out of commission because of waterlogging.
Steve Swift and Doug Titterington, of Bedale, came in with just one point fewer, enabling them to take second place from three pairings - Phil Hudson and David Hartley (Harrogate), Dave Edmundson and Bert Harrison (Ripon City) and Geoff Coles and Richard Megson (Bedale).
Hudson and Hartley took third place on countback.
Eventual runners-up Swift and Titterington had teed off at 9.30am and held the lead for almost two and a half hours.
Seven pars on the homeward run looked to give them a good chance of winning any possible back-nine countback, but Greenwood and Garbutt had six pars plus one birdie to make such a conclusion unnecessary.
Temporary greens were in play at all but the 15th hole and use of mats was compulsory through the greens.
Union press officer Gordon Carr has a granddaughter, Rosie, who is undergoing treatment for leukaemia at Leeds General Infirmary.
Normal entry of £30 per pair was intended to be reduced to £25 at Knaresborough because of play being restricted to 16 holes.
But entrants paid the usual fee, with the additional £5 per duo helping raise £140 for the Candlelighters charity, which funds research, family holidays, grants, and essential additional services within the hospital as well as providing support for families battling children's cancer.
This followed a collection of £125 contributed recently by people attending the union's Founders' Dinner.