The victory over in-form Hull moved Blues up to within two points of second place in PDL Northbcfc.com
George gave Blues the breakthrough in the 50th minute, following in after a Josh Andrews shot was parried.
And although Blues could have made the rest of the game more comfortable having created other openings, it wasn't until Burke burst through to slot just inside the post with nine minutes to go that matters were decided.
It wasn't an easy night at the East Riding FA ground for Blues against opponents who were seeking a fifth straight PDL victory, having also not conceded in that spell.
A awfully bobbly pitch was certainly a test of touch and decision-making, but Blues hardly faltered in either respect.
Ryan Stirk once again dictated so much of the play, Moha Ramos was safe and sound while Nico Gordon was classy at the back. Bernard Sun made his first competitive start for the Under-23s and worked diligently as well as provided some good linking passes.
The first-half was predominantly a battle to gain control and Blues had much more possession and stayed true to their passing game.
There was little goalmouth action, with Matty Jacobs firing close for Hull before Blues created a very good chance.
Goalkeeper David Robson sliced an intended clearance horribly as the ball bobbled just before contact and it was retrieved wide on the left by George. He hared on towards the byline and pulled the ball back for Andrews, but he couldn't get a clean enough contact on his sidefooter and it went straight at Robson.
After the break it was a different story.
Five minutes in Blues took the lead when Burke was quick to stop Hull repelling an attack. First to a pass near halfway, he fed Andrews to the right of the area and he got a low shot away at goal; Robson kept the attempt out but George was onrushing to thump the lose ball home from close range.
Burke - fresh from his First Team involvement on the bench in the FA Cup two days earlier - next played a ball in behind for George down the left channel and the 'keeper did well to beat away his effort, having come out sharply to shorten the distance between them.
In the 59th minute a lovely pass by Sun enabled Kyle Hurst to veer inside, swerve onto his right foot and plant a curving shot just wide.
Blues were well in the ascendancy but Hull dragged themselves back into things.
Billy Chadwick's half-volley on the turn flew just over the crossbar before Will Jarvis wriggled his way into the box only for Ramos to gather his eventual strike.
With 16 minutes left Hurst almost scored a stunner: Kane Thompson-Sommers clipped a great ball into the area and Hurst took it in the air with his first touch and tried to nudge it past the 'keeper with his second, all the while on the run, but Robson made a spectacular save.
Ramos was next called into action after punching clear a Hull corner; the ball was put back into the area, a scramble ensued and Ramos reacted smartly to narrow the angle and block Chadwick's blast in the thick of a crowd of bodies.
Then came the goal that decided the contest.
After some approach play high on the left, Hull felt they had the danger covered but Burke drove onto a loose ball, continued straight into the area and although his initial left foot effort was blocked, he got a second bite as it rebounded back to him and he promptly steered it past Robson with his right.
A deft touch by Thompson-Sommers next set up Hurst down the middle and he was not too far away from adding a third for Blues.
Hull's last response came from James Berry, who connected on the full as the ball reared up outside the area, but Ramos stretched his frame to execute a good tip over save.
Blues: Ramos, Forrest, Burke, Gordon, Roberts, Stirk, Thompson-Sommers, Sun (Campbell 66), Hurst, Andrews, George. Subs not used: Rouse, Baker, Hilton, Fernandez.