Mickey Mellon's side arrived at Kenilworth Road on Thursday knowing a two-goal victory would see them replace Wycombe Wanderers as league leaders.
However, Shrewsbury could consider themselves somewhat fortuitous to come away with a point as Luton enjoyed the better of proceedings.
The hosts hit the post through Jake Howells early on and applied significant late pressure following the 70th-minute dismissal of Shrewsbury defender Nathaniel Knight-Percival for a second bookable offence.
Yet visiting goalkeeper Jayson Leutwiler held firm, making a number of impressive stops to ensure the match finished goalless.
Shrewsbury remain third in the table, behind Wycombe and Burton Albion having played a game more, while Luton leapfrog Newport County into fourth.
‘It was without a doubt one of the most important matches that I played in my career. It wasn’t just Champions League football – it was a whole club at stake’: Ex-Chelsea star opens up on key game which changed the Blues' fortunes forever
'I was Arsenal captain and really enjoyed it, but when Man City come calling, you have to listen': England international reveals reason for swapping London with Manchester
