Jean Louis-Valois dribbled through the City defence but shot straight at Musselwhite soon later.
City's closest attempt of the day came inthe 20th minute when Mike Edwards' header from a corner was cleared off the line.
But Town took the lead minutes later, with the unmarked Steve Howard thumping in a header from Taylor's cross.
7 minutes from half time Dean Crowe pounced when Jason Van Blerk couldn't get anything on Taylor's long pass. Crowe rounded Musselwhite, and despite a last-ditch sliding tackle from Van Blerk, the ball trickled over the line to make it 2-0.
Whitmore and Holt were introduced early in the second half, with Bradshaw and Williams going off.
It was curtains 11 minutes from time, with Howard meeting Taylor's cross in front of the 2000 travelling Hatters fans. Supporters from the other three sides of the ground left in mass numbers.
Howard got his third in the final minute to make it 4-0, and a "devastating" start for new City boss Jan Molby.
He said afterwards: "I knew that all was not well but I didn't think it was as bad as our performance showed today.
"There weren't any positives and all aspects of our play simply weren't good enough.
"You look at it and ask the question what did we do well. Did we defend well? You'd have to say no. Did we compete well? Again, the answer is no. Did our fitness stand up to the pace of the game? Most definitely not. It was all very poor.
"But I'm confident that we'll improve next season and it doesn't take a lot of working out that there are lots of things to work on, including some of the basics."
City line-up (4-5-1): Musselwhite; Edwards, Mohan, Greaves, Van Blerk; Lightbourne (Norris), Petty, Sneekes, Williams (Whitmore), Bradshaw (Holt); Alexander.
Un-used subs: Glennon, Philpott.