Classy finishes from Eden Hazard and Diego Costa put the Premier League leaders two goals in front after only nine minutes at the KC Stadium on Sunday.
Hull responded impressively to those early blows and two goals in the space of 74 seconds brought them back on level terms with less than half-an-hour played.
First, Ahmed Elmohamady halved the deficit before Abel Hernandez took advantage of a dreadful mistake from Chelsea goalkeeper Thibaut Courtois to equalise.
Loic Remy had the final say, though, scoring the 77th-minute winner with his first touch after replacing the injured Costa with a shot that Allan McGregor really ought to have saved.
Defeat leaves Hull still only three points above the relegation zone, but Bruce was encouraged by his side's performance.
He said: "I think we deserved something from the game, we are disappointed to be empty handed,
"You have to look at our performance, especially having been two goals down after nine minutes. You look for a response in that situation and we got one.
"The players put in one hell of a shift and to have something like 19 shots against a side as good as Chelsea tells you how well we played."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.