Bruce, who distanced himself from the manager's job at Newcastle United this week, appeared to be in a precarious position as Hull went into the clash on the back of one league win in 12, but they were well worth all three points at the KC Stadium.
The home side saw an early penalty claim turned down as the eye-catching Abel Hernandez was tripped, though that ultimately mattered little as Ahmed Elmohamady nodded Hull ahead just after the half-hour.
And the second was not too far behind, as former Everton striker Nikica Jelavic made the most of slack defending after an admirable display of craft from Hernandez.
Everton manager Roberto Martinez had made seven changes from the side which lost to 3-2 to Newcastle United, but the Merseyside club lacked cutting edge in attack as the likes of Kevin Mirallas disappointed.
The visitors failed to turn second-half possession into anything tangible and saw Antolin Alcaraz sent off late in the game for a second bookable offence to compound their misery.
Hull were frustrated not to be awarded a penalty after three minutes, as Hernandez - one of four changes for the hosts - was tripped just inside the area by Gareth Barry, but referee Kevin Friend only gave a free-kick.
Bruce's men continued to give Everton very little room for manoeuvre and effective pressing from Hernandez just two minutes later helped the Uruguayan to rob Ross Barkley of possession, before forcing Joel Robles into action from 25 yards.
Liam Rosenior replaced the injured Andrew Robertson soon after and had a big hand in breaking the deadlock.
With the visitors looking shaky at the back Hull capitalised in the 33rd minute, Elmohamady guiding Rosenior's left-wing cross past Joel with a delicate header.
And Hull went into the break two goals up as the impressive Hernandez played a clever pass over his own head for Jelavic, who looped an effort over Joel after marching clear of the static Everton defence two minutes before half-time.
Clearly unimpressed with his team's first-half display, Martinez replaced Mirallas and Muhamed Besic with Romelu Lukaku and Bryan Oviedo at half-time.
Those changes did little to stifle Hull's attacking threat, however, and they nearly added a third three minutes into the second half, only for Hernandez to scuff wide after a goalmouth scramble.
Ross Barkley drew a save from Allan McGregor after neat footwork beat three Hull defenders, with Harry Maguire - introduced after Rosenior was carried off with a hamstring injury - producing a crucial block with 25 minutes to go, denying Steven Naismith from 12 yards.
Everton piled men forward in a desperate attempt to salvage a point at the death, but their chances suffered a fatal blow in the 86th minute as Alcaraz received his second yellow card for a bodycheck on Jelavic and Hull went on to claim all three points.
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.