The jubilant Shrews were left to celebrate wildly after striker James Collins scored the game’s solitary goal in the 38th minute.
The visitors were unable to get back on terms, and the result ensures that Shrewsbury are promoted with other scores going their way.
Already promoted Swindon were crowned the League Two champions as they thrashed Port Vale 5-0 at the County Ground.
Paul Benson scored two, with Aden Flint, Alan Connell and Matt Ritchie all on target for Paolo Di Canio’s men.
At the other end of the table, Macclesfield Town were relegated after they suffered a 2-0 defeat at home against Burton Albion.
Late goals from Calvin Zola and Jacques Maghoma ensured that Macclesfield slipped out of the football league.
It was also not a good day for third-placed Crawley Town, however, as they suffered a 3-0 home defeat to relegation-battling Hereford.
A brace from substitute Yoann Arquin and a goal from Joe Colbeck ensured the points for Hereford – who are now just two points from safety - with Crawley missing the opportunity to move clear of Torquay United.
Barnet’s 4-0 win at home against AFC Wimbledon proved more important given Hereford’s victory, and it sees them stay out of the relegation zone.
Plymouth moved five points clear of safety as they claimed a 2-2 draw at Morecambe, while Northampton also finished with a point after a 1-1 draw with Gillingham.
Cheltenham beat Bradford 3-1 at Whaddon Road to consolidate their place in the play-off places, while a 2-0 away win for Southend at Oxford United left them in fifth.
Crewe ended the day in seventh with a 1-1 draw at Torquay, while Bristol Rovers thumped Accrington 5-1 at the Memorial Stadium and Aldershot shared the points with Rotherham in a 2-2 draw.