2 minutes later, the ball went in at the other end with a much less clear-cut chance. Stuart Elliott did well to take the ball down the left wing, and his dipping cross went over Dino Serentet and inside the far post to give City the lead in a bizarre fashion.
Elliott then came close to connecting with a header in a more conventional attack, and had another header saved before getting booked for raising his foot to block a Serentet clearance.
Steve Howard forced another great save out of Myhill with a swerving 25-yard shot.
As well as stopping goals going in, Myhill also played his part as City made it 2-0 in the 22nd minute. His long clearance caused confusion between Luton defender Paul Underwood and his keeper. They both got in each other's way, leaving Delroy Facey with an easy chance. He side-footed it and Sol Davis on the line couldn't stop it going in.
Facey went wide with a long-range effort after being found by Nick Barmby, and Stuart Green was later off target as well with a shot.
Luton found the back of the net but had it disallowed. Kevin Foley's deflected shot beat Myhill, but Howard was already ruled to be offside.
Moments later, the visitors were left scratching their heads as they found themselves 3-0 down. Facey's long-throw made its way to Elliott who tapped it in from close range after 33 minutes.
Howard shot over with another good Luton chance, while Barmby went just wide with a shot from a clever corner routine.
5 minutes into the second half, Price had a shot saved low down at the near post after Green and Barmby combined to set him up.
The Hatters were reduced to ten men just after the hour mark, Kevin Nicholls dismissed for elbowing Elliott in an aerial challenge.
With an extra man, City completely dominated and could have added to their three-goal lead. Green was off target with a left-footed shot after good build-up play, and Michael Keane almost got himself on the scoresheet after coming on but was denied by Seremet.
The 3-0 win, in front of an 18,575 crowd at the KC Stadium, sees City go up to 3rd in the table, level on points with 2nd-placed Bradford, and 4 behind Luton who stay top despite losing their last three games now.
City line-up (4-4-2): Myhill; Joseph, Cort, Delaney, Edge; Price (Keane 73), Green, Lewis, Elliott; Barmby (Allsopp 73), Facey (Walters 81).
Un-used subs: Brock, Hinds.