Tows bounced back from their drubbing at Derby to notch up a first win in Midlands 1 East.
They flew out of the starting blocks and, despite having a strong wind in their faces, raced to a 19 point lead at half time.
Flanker Yuon Skelton, whose work is unstinting, was the first to score, crossing in the first minute. Matthew Yuill converted.
Tows became bogged down for a while as Nuneaton stuck the ball up their collective jumper and earned a penalty as reward.
Towering No 8 Craig Holton outpaced the defence with a trademark striding run to snag a third score.
He added another soon after when Goodman cut through and Tows turned round 22-3 up.
It was to be a topsy turvey game however. With the gale now favouring the hosts, the large crowd at Greens Norton Road expected the second half to be a formality.
All Tows needed to do was to kick to the corners to keep Nuneaton pinned back and under pressure but to do that they needed the ball.
Nuneaton starved them of it and rumbled forward relentlessly through their heavier pack.
Tows conceded a string of penalties and failed to defend from a quick tap taken inside the 22 to allow the visitors back into the game through a converted try.
Now just 12 points ahead, Tows lost their skipper Liam Wilkinson to a yellow card when the referee ran out of patience with the side’s repeated offending.
Nuneaton rumbled forward again and bagged a second try to make it 22-15 to leave the crowd on the edge of their proverbial seats.
Tows squandered a clear chance to score late in the game but managed to hang on win their first League game following promotion last year.
John Ashby and Ben Roe both made sound debuts.