Matt Thornhill and Kane Richards ensured a fourth straight win for Steve Chettle’s side in a game delayed by nearly an hour as Yates received lengthy treatment.
An otherwise innocuous situation soon turned nasty when a floored Yates was caught with the boot by his own defender clearing his lines and required urgent medical attention.
The game was initially halted, until a temporary postponement by the officials saw both sides return to the dressing rooms awaiting news on Yates’ condition before he was consciously stretchered off to hospital.
Trinity’s injury woes continued as former Mansfield Town striker Nyle Blake pulled up with a hamstring injury, although it was his side who looked the most troublesome.
Impressive all night, full-back Joe Wilson fizzed in a low cross on the half-hour mark, though no-one in blue could read the danger before his cute, reverse pass found George Hornshaw who blazed well over.
Non-threatening to this point, Basford’s own Wilson, Ryan, did well to win a corner off Charlie Jemson and a well worked routine saw Thornhill emphatically flick home at the front post for the go-ahead goal.
He nearly added a second five minutes after the break when O’Connor did well to shimmy round Jemson from Wilson’s throw and his pass found the midfielder who could only poke into the side netting from a tight angle.
Just short of the hour, another shot was blocked which led to another corner and Wilson, having a second bite and with acres to assess, put in a deep cross which was trapped superbly by Brad Gascoigne who fired back across, and Richards bundled home a second to extend United’s unbeaten run to seven.
Gainsborough will host Stalybridge Celtic on Saturday in a rearranged league encounter.
Gainsborough: Matt Yates (Jack Gibson 20’), Joe Wilson, Toby Gould (Lewis Butroid 58’), Hayden Cann, Charlie Jemson, Isaac Rice, George Hornshaw, Liam Waldock, Brad Grayson, Alex Wollerton, Nyle Blake (Harry Jessop 26’)