Michael Jackson's men knew that only a victory could take their relegation battle to the last weekend, but it was the visitors who came away with the points and in the process confirmed their spot in the play-offs.
Shrewsbury were given hope when Jon Taylor opened the scoring in the sixth minute, but Darren Ferguson's side were 3-1 ahead inside half an hour thanks to Conor Washington's double and a Lloyd Isgrove strike.
Tom Bradshaw reduced the deficit shortly before half-time, but the home side were hit on the break when Josh McQuoid scored in second-half injury time to end Shrewbury's two-year stay in the third tier.
Elsewhere, Notts County moved out of the relegation zone as goals from Alan Sheehan and Callum McGregor were enough for a 2-0 victory over Swindon Town at Meadow Lane.
The visitors' misery was further compounded by the red cards shown to Troy Archibald-Henville and Nathan Thompson in an ill-tempered finish that ensured Swindon's slim play-off chances were finally extinguished.
Time is fast running out for Carlisle United to beat the drop after they slipped to a 1-0 home defeat to Oldham Athletic, who officially confirmed their safety, while goals from Kevin Lisbie and Chris Dagnall saw Leyton Orient win 2-0 at home to Tranmere Rovers, who fell into the bottom four.
Crewe Alexandra are just one place and one point outside the relegation zone, though a 0-0 draw at Bristol City may yet prove to be crucial in their battle to stay up.
Freddie Sears grabbed a brace as Colchester United all but ensured they will remain in League One after a 4-1 rout of already promoted Brentford.
Colchester can still be caught by Tranmere and Carlisle but possess a far superior goal difference over both.
Coventry City are mathematically safe following a 1-1 draw at home to champions Wolves, who reached 100 points for the campaign with a draw.
In other matches, Rotherham United - who will contest the play-offs - earned a dramatic 2-2 draw at home to MK Dons thanks to late goals from Michael O'Connor and Alex Revell, the visitors finishing with 10 men when Brendan Galloway saw red, while Preston North End are also building momentum ahead of the play-offs with a 3-1 victory over Gillingham at Deepdale.
Already relegated Stevenage salvaged some pride in a 3-2 win over Walsall, while Bradford City saw off Crawley Town in a 2-1 win.
