The £4million midfielder, who was suspended for the defeat at Derby on Saturday, struck midway through the second half as the Hammers moved level on points with Championship leaders Southampton.
Sam Allardyce's side had been frustrated by in-form Coventry goalkeeper Joe Murphy for 65 minutes, but he was finally beaten when skipper Nolan headed his seventh goal of the season.
It was only the Hammers' second win in six attempts but they are now only being kept off top spot on goal difference by Saints, who have been wobbling themselves of late.
The Sky Blues had their chances, though, but top scorer Lukas Jutkiewicz could not add to his tally of nine goals.
The visitors created the first opportunity when Gary McSheffrey raided down the right and crossed towards Chris Hussey, whose first-time shot flew narrowly wide.
West Ham were denied by Murphy twice in quick succession, saving from Nolan with his feet and from the ensuing corner keeping out Jack Collison's snap-shot.
The hosts were dominating possession but City were dangerous on the break and Jutkiewicz should have done better with a free header from Gary Deegan's cross which he nodded wide.
At the other end Julien Faubert's volley flew wide and Papa Bouba Diop's header was deflected clear before the interval.
Early in the second half Jutkiewicz squandered another good chance after Faubert made a hash of his clearance.
Jutkiewicz had more time than he realised in the penalty area and headed the ball meekly over the top when he could have allowed the ball to drop and taken a shot.
But the City goal was at times leading a charmed life with James Tomkins heading Mark Noble's corner wide and Sam Baldock also off target from Carlton Cole's cross.
Murphy then produced two stunning saves to deny the Hammers, first pushing Baldock's shot onto the underside of the crossbar and then palming away a powerful header from Collison.
The loose ball fell to Tomkins but the defender skewed his shot into the ground and it bounced over the top.
But the breakthrough eventually came when Tomkins beat Hussey in the air to head George McCartney's cross back across goal where Nolan was on hand to nod it past Murphy and into the net.
It should have been two minutes before the end after Richard Wood under-hit a backpass but Murphy saved well from Frank Nouble and Noble put the rebound wide with the goal gaping.
And Hammers hearts were in their mouths when Carl Baker's shot was deflected onto the crossbar as the hosts survived a nervy ending.
