The centre-back ensured York triumphed at home for only the third time in 2014-15. But it could prove the most crucial victory of the campaign, as it moved the club seven points clear of their visitors at the foot of the table.
York also now boast a five-point cushion over second-bottom Tranmere.
During a cagey first half, Robins striker Shaun Harrad had the best chance to score but headed weakly at recalled York goalkeeper Michael Ingham from four yards.
After the break, York got on top with Michael Coulson hitting a post from a firmly-struck free kick. Half-time substitute Stephane Zubar also had a ‘goal’ disallowed and a header cleared off the line by Matt Richards.
Winfield made no mistake on 73 minutes, however, climbing high to meet Luke Summerfield’s corner.
Delighted York manager Russ Wilcox hailed his team’s efforts over the last three matches with seven points collected from a possible nine, but also warned against any complacency ahead of Easter Monday’s trip to Oxford United.
He said: “We must keep our foot on the gas. Bristol Rovers probably thought they were safe at this stage last season but ended up going down.”
York winger Josh Carson missed the match in hospital with severe concussion following a Saturday night incident that is being investigated by police.
York City: Ingham, Lowe, Winfield, McCombe (Zubar, 46,), Halliday, Summerfield, Penn, Coulson; Platt (Miller, 69), Hyde, Coulthirst (O’Hanlon, 90). Unused substitutes: Mooney, McCoy, Ilesanmi, Montrose.
Cheltenham Town: Carson, Vaughan, Brown, Packwood, Braham-Barrett, Wynter, Richards, Mills (Hanks, 69), Burns, McDonald (Haynes, 74), Harrad (Manset, 74). Unused substitutes: Taylor, Gould, Deaman, Berry.
Referee: K Wright (Peterborough).