Brothers Rik and Jake Hobbs combined to put 15 points on the board while Oti Pifeleti and Dave Evans also contributed with a try-a-piece.
Fly half Rik Hobbs opened the scoring as he slotted home a penalty to make it 0-3.
However, his opposite number levelled the scores with a penalty of his own to make it 3-3 after 16 minutes.
The lead didn’t last long as J. Hobbs scored the first try of the match two minutes later, brother Rik converted to make it 3-10.
Pifeleti extended Luton’s lead in the 26th minute as he added a second try for the visitors, this time Hobbs failed to convert.
Oadby Wyggestonians’ fly half kicked a second penalty between the posts 10 minutes before the break to make it 6-15.
Dwayne Duffy was shown a yellow card in the opening stages of the second half and the home side took advantage of the extra man as they scored their first try of the match, closing the gap to just four points, the kicker failed to convert.
Any hopes of a come-back for the table-toppers was put to bed as Luton scored two consecutive tries, the first from R. Hobbs the second from scrum half Evans, R. Hobbs couldn’t convert either.
The home side’s second try of the game made it 16-23, however it was nothing more than a consolation.
Speaking afterwards Luton captain Ryan Staff said: “That was a top draw performance from both our forwards and backs, our great defence set the tone for the match.”
Luton could move into second with a victory in their re-arranged fixture with Market Harborough which will take place on Saturday, looking ahead to the massive fixture Staff added: “We are keeping our focus from the Oadby Wygestonians game and looking forward to it.”