Junior English headed wide from an Andy Ducros free-kick in a game where chances were few and far between.
Seconds before half-time the crossbar prevented the hosts from taking the lead as a Robert Dale header thundered off the woodwork.
After the break it was all about the home side and they opened the scoring on 54 minutes, Gareth Williams curling a free-kick past keeper Danny Crane and into the top corner.
Simon Todd doubled Blyth's advantage with 20 minutes remaining as he fired in the rebound from Dale's palmed effort.
It needed a goal-saving clearance from Theo Streete to keep out a Jed Dalton chip on 81 minutes as Spartans continued to press.
The game was wrapped up in the 83rd minute though when striker Dale converted a penalty following a foul on the impressive Dalton. ..SUPL: