The PA system at Broadhall Way aptly played us out to the theme to 'Ski Sunday' as temperatures dipped below freezing.
And in fairness there was little goalmouth action to warm fans in what was nevertheless a competitive FA Premier Reserve League encounter.
Milenko Acimovic ended a probing Rohan Ricketts run with the first shot on goal after three minutes but within a matter of seconds Neil Sullivan had to be at his best to deny Andrew Hall from close range.
A couple of flashes of skill from Acimovic almost opened the door but it was Sullivan who was forced into action again next, a magnificent save to his right to deny Hall's snap shot again after Julian Joachim's break down the left.
John Jackson looked certain score from Mark Hughes' cutback after 42 minutes but his goalbound shot struck the unknowing Calum Davenport and bounced to safety.
City opened the scoring just before the break. The goal evolved around Eustace who initially saw his volley deflected a yard wide but was on the spot to smash home when Davenport headed the ensuing corner back into the danger area.
The teams traded shots at the start of the second half, Ricketts firing over and Matt Etherington burst through onto a loose ball on the hour but visiting goalkeeper Fabien Debec was our sharply to meet him.
Etherington soon turned creator, squaring to Acimovic in the box but the Slovenian appeared in two minds on how to take the chance and ended up flicking the ball over.
Eustace's shooting ability tested Sullivan to the full after 67 minutes, a full-length, but comfortable, save to his left from a 22-yard drive. Davenport's flicked header then drifted inches wide.
Hughes shot was deflected wide after 77 minutes and young substitute Kieran McKenna had the chance to score with his first touch in reserve football when Etherington squared in front of goal, Debec blocked McKenna's effort and Ricketts' follow up hit a combination of McKenna and Etherington in front of goal - typical of the night.
Line-ups: Spurs: Sullivan, Hughes, Thatcher, Toda, Henry, Thelwell, Ricketts, Acimovic (McKenna, 81), Etherington, Jackson, Galbraith. Subs: G Kelly, Hodges, Jenkins, Hicks.
Coventry: Debec, Whing, Stanford, Cooney, Davenport, Eustace, Hall, Strachan, Jephcott, Joachim (May, 45), Noon (Fowler, 64). Subs: Brush, Osbourne.
John Eustace's strike proved the difference as a youthful Coventry City edged out our reserves in the bitter cold at Stevenage Borough on Monday night.