However, Mark Robins' men sealed the deal in stoppage time when Callum O'Hare tapped home Coventry's third of the game and his fourth Championship goal of the season.
Sky Blues upset the odds again
A theme of life under Robins for Coventry has been the sides ability to take the game to the top teams in the division.
This has been showcased time and again this season, and Sunday's win away in West London was just the latest example of that.
It completes a league double over Fulham for the Sky Blues and it likely raises questions amongst the squad and fans alike about what might have been achievable this season had City not been so inconsistent.
And although Coventry have still surpassed expectations this season, it is victories like this one which will leave a bittersweet taste as the end of the season approaches.
Mitrovic has record denied
Fulham's talisman Aleksandar Mitrovic could have been well on his way to a piece of Championship history with a goal on Sunday.
Had he took his Championship goal tally to 39 against Coventry, Mitrovic would have been looking likely to score against every single opponent in a single Championship season.
⚽️ The full list of Championship clubs Aleksandar Mitrovic has 𝗡𝗢𝗧 scored against this season:— The Championship Chat Podcast (@Champchatpod24) April 7, 2022
Preston North End
Fulham still have to play all of them. 👀
He couldn't, could he? 😉#CCP | #FFC pic.twitter.com/GIFuAYN7VX
Unfortunately for the Cottagers, the Serbian international was unable to find the net against the Sky Blues as they fell to defeat.
Although, there can be no doubt that the forward has still had an astonishing season, breaking Ivan Toney's record of 31 Championship goals with 14 games still to play.
Mitrovic is currently averaging above a goal every game, notching a tally of 38 goals in 37 games for Fulham.
Hamer impresses once more
Firstly, his wicked set-piece delivery was a handful for Fulham and it led to the Sky Blues taking the lead.
Hamer's corner was teasingly whipped in at the near post and flicked into the far bottom corner by Rose, leaving Fulham dumbfounded as they were unable to defend the delivery.
Normal service was the resumed for the Dutch-born Brazilian on 80 minutes, as he picked up his 14th yellow card of the season.
And finally, Hamer showcased his class once more as O'Hare wrapped the game up in stoppage time.
He beat Marek Rodak to a loose ball on the right side of the Fulham penalty area, before having the presence of mind to look up and pick out O'Hare who tapped in to seal the deal for the Sky Blues and give Hamer his eighth assist of the Championship season.
Although Hamer signed a contract extension until 2024 at the start of March, Football League World were also reporting that Celtic and Rangers remained interested in the midfielder around the same time.
Though the new contract likely signifies that Hamer will stay with the Sky Blues, there are no guarantees that Coventry will be able to fend off the lure of European football with either of Glasgow's biggest clubs.