The full-back who underwent abdominal surgery in September put in a typically all-action display including a goal-saving block in the second half as we overcame a City side that sat joint-top of the Barclays U21 Premier League at the start of play.
Bongani Khumalo also returned from a serious knee injury sustained on international duty in March while Coulthirst was able to take the field again in a Spurs shirt as part of his youth loan at Southend.
While Coulthirst grabbed both goals, the last-minute hero was goalkeeper Luke McGee, who saved George Evans' penalty to preserve the win in injury time.
City were determined to play out from the back but the high press of Coulthirst, Nathan Oduwa and particularly Will Miller kept them penned in their own half in the first half. We won back possession on numerous occasions and the visitors rarely threatened our penalty area.
At the other end, Josh Onomah, Miller and Coulthirst all tried their luck from distance before the opener on 28 minutes.
Oduwa's cross from the right looped up to the far post where Coulthirst rose powerfully to power a downward header past Angus Gunn at the far post.
City's first chance came on 36 minutes when McGee was out sharply to block Sinan Bytygi.
City took the corner quickly and Bytygi had a sight of goal but dragged wide.
A minute later and it was 2-0 and a fine team goal involving intricate passing between Walker, Onomah, Oduwa and Miller that ended with Onomah finding Harry Winks who in turn crossed for Coulthirst to convert from close range.
Coulthirst had a chance of a hat-trick before the break but headed straight at Gunn from Winks' corner.
City made a change at half-time with Bersant Celina on for Jordy Hiwula and came out a different side after the break.
They dominated the early exchanges and carved out three chances - Brandon Barker's shot touched wide by McGee on 49 minutes, Walker's goal-saving block on the line denied Celina from Bytygi's cross on 52 and then Celina mis-hit his shot 12 yards out.
We saw out that early storm though and Coulthirst came close to his hat-trick again on the hour after Walker's burst into the box and cross that looped up and was met again by Coulthirst at the far post, this time his header just over.
Momentum had changed in the game though and City pulled a goal back on 70 minutes when Celina turned home Bytygi's cross from 15 yards.
City continued to press but we held firm, marshalled by Khumalo and Dominic Ball, who switched from central defence to midfield in the final 10 minutes as Cameron Carter-Vickers came on for Filip Lesniak.
After keeping City at bay until the 90th minute, the vistors were awarded a penalty when Connor Ogilvie was judged to have upended Bytygi. Evans stepped up, McGee guessed right and ensured the three points were going back to N17.
Spurs: McGee; Walker (Walker-Peters, 67), Ball, Khumalo (C), Ogilvie; Lesniak (Carter-Vickers, 81), Winks; Miller (Sonupe, 62), Onomah, Oduwa; Coulthirst. Substitutes (not used): Voss (GK), Akindayini.
Manchester City: Gunn, Smith-Brown (Horsfield, 86), Maffeo, Evans, Tasende, Glendon (C), Ambrose, Ntcham (Byrne, 89), Hiwula (Celina, 46), Bytygi, Barker. Substitutes (not used): O'Brien (GK), Oliver.