The French striker, out for more than two months with a troublesome groin injury, hit the opener in the 61st minute with his only sniff of goal all night, and looks ready to make his Premiership comeback in the home clash against Southampton next Monday.
Fredi was part of a strong Hammers side that included no fewer than seven players with first team experience, as Don Hutchison stepped up his recovery from a serious knee injury and the likes of Gary Breen, Scott Minto, Richard Garcia and Laurent Courtois were all given opportunities to stake their claim for first team action.
In a lively encounter at the Boleyn Ground that produced three bookings for the Hammers - picked up by Minto, Hutchison and Brent Rahim, Hammers looked to be heading for all three points thanks to Kanoute's strike, but Coventry midfielder Craig Pead struck an excellent goal with four minutes remaining to earn his side a share of the points.
After a scrappy first half in which neither side created any clear cut chances - Hammers' best effort came when Courtois fired an effort just wide in the 13th minute - the hosts took the lead just after the hour when the nippy French winger threaded a perfectly measured pass through to his fellow countryman Kanoute, who rounded keeper Montgomery and slotted into an empty net.
The goalscorer was then immediately replaced, as planned, by Titi Camara, who came close to adding a second when his low shot took a deflection and almost deceived Montgomery, who did well to adjust himself and gather the ball.
Coventry had never really looked like threatening and had their most dangerous player - the former Arsenal youngster Jay Bothroyd - kept reasonably quiet by the impressive Anton Ferdinand, but grabbed the equaliser against the run of play in the 86th minute when Pead ran on to a reverse pass and beat Raimond Van der Gouw with a superb left foot finish.
The goal once again denied a West Ham team that long-awaited first win of the season at Upton Park - a feat that will hopefully arrive with a Kanoute-inspired victory against the Saints next Monday.
Hammers: Van der Gouw, Byrne, Breen, Ferdinand,
Minto, Hutchison, Garcia, Rahim, Courtois, Kanoute (Camara 63),
Sofiane. Subs unused: Forde, Britton, McMahon, Laws, Lumsden.
Coventry: Montgomery, Ford, Quinn, Betts, Shaw,
Pead, Fowler, Strachan, Bothroyd, Pipe, Hall. Subs unused: Brush,
Miller, Stanford, Osbourne, O'Donovan.