Second-half goals from Coulson and John McCombe, giventheir first action of the season due to injury and being out of favour, respectively, had put York in the ascendancy.
Wilcox admitted replacing Coulson on 65 minutes proved a turning point as Cambridge hit back through Mark Roberts and Barry Corr.
With Coulson in following his recovery from a groin operation, the Minstermen’s chief explained that he had no choice.
“Michael brought that bit of quality he possesses back into the group,” said Wilcox. “It was a very good finish for his goal and he’s a key player for us. His substitution was probably the game’s turning point but the bigger picture is he has had a long spell out and we have to be careful with him. We knew he wouldn’t get through 90 minutes.
“It was an enforced change and he played ten or 15 minutes longer than I wanted him to.”
Coulson opened the scoring on 50 minutes, firing in from 15 yards after Rhys Turner had competed for the ball following Marvin McCoy’s low right-wing cross.
Four minutes later, McCombe curled in from the edge of the area after Turner’s lay-off.
Roberts made it 2-1 on 71 minutes when he drilled in from eight yards and his 81st-minute shot was then saved by Scott Flinders only for Corr to pounce from close range and upset home fans.
York City: Flinders; McCoy, Lowe, McCombe, Ilesanmi; Penn, Collins, Berrett; Coulson (Godfrey, 68), Turner (Sinclair, 76), Straker (Carson, 79). Unused substitutes: Ingham, Swan, Tutonda, Thompson.
Cambridge: Beasant, Legge, Roberts, Taft, Taylor, J Hughes, Dunk (Gaffney, 46), Donaldson (Berry, 58) L Hughes, Corr. Unused substitutes: Omozusi, Simpson, Morrisey, Chiedozie, Newton.
Referee: B Toner (Lancashire).
Man of the match: Mark Roberts.