News broke of Arveladze's departure just hours before the Friday night contest at the MKM Stadium, with owner Acun Ilicali citing a difference of opinion surrounding the future direction of the team as a reason for the decision.
However, with caretaker boss Andy Dawson in temporary charge for the night, the Tigers failed to muster a significantly improved performance following Arveladze's sacking as they slumped to a fifth straight defeat.
Hull are now also without a goal in their last four outings, a run of form which has left them 20th in the table and in danger of dropping into the relegation zone this weekend.
While goals at the right end have been hard to come by, it was a Hull player who put the ball in the back of the net for the opening goal of night as Alfie Jones beat his own keeper after only six minutes.
There may have been an element of fortune to the opener for Luton, but there was nothing lucky about their second just before half time as Henri Lansbury lit up the contest with a stunning long-range strike.
The ball broke to the midfielder around 30 yards from goal, and he did not hesitate to drill a sweetly-struck first-time effort low into the bottom corner.
Hull struggled to muster anything in reply and a miserable day for the club ended with them failing to have a single shot on target in front of their own fans.
The result sees Luton leap into the playoff places having now lost just one of their last seven games, climbing six places into the fifth ahead of the rest of the weekend's games.
It is the first time that Luton have won back-to-back games since April, and they will next look to make it three on the bounce at home to Huddersfield Town in midweek.
Hull, meanwhile, will hope to stop the rot at home to Wigan Athletic on Wednesday night.