The Shrews had scored 12 goals in their last three matches and had not lost in their last seven.
Following an impressive 4-1 win on Saturday, Paul Simpson's side were understandably favourites to take the points.
But they conceded two sloppy goals in the space of four first-half minutes as they slumped to defeat.
Terry Gornell netted as early as the second minute, before Paul Mullin headed in a second in the sixth minute to surprisingly put the hosts in control.
Accrington lost Phil Edwards in the 18th minute after an unexpected injury, but it didn't halt the home side's rhythm as they pushed for another goal to put the contest out of reach.
But Ben Davies scored with a 68th minute strike to give the visitors hope.
However, Accrington clung on for the point and proved once again that they can compete with the best in the division.
As early as the second minute, Gornell rifled a shot past Shrewsbury keeper Luke Daniels.
In the eighth minute, Paul Mullin had a shot saved by Daniels, while at the other end Shane Sherriff fired over as the visitors looked to reduce their arrears.
Phil Edwards went close for Accrington, before Gylfi Sigurdsson shot wide for Shrewsbury.
Eventual goalscorer Davies squandered a good chance on the quarter hour mark, before John Miles had a shot saved.
Both sides battled to impose themselves before Sherriff missed the target on the stroke of half-time.
Grant Holt saw a header well saved by Kenny Arthur, before Miles had a shot saved.
In the 64th minute Chris King fired wide, but the hosts were hit with a sucker punch when Davies netted to give his side hope.
But despite their best efforts, Simpson's men were upset by John Coleman's side in a turn up for the books.