The Seasiders' seven-match unbeaten run was ended after a seven-goal thriller at the Mounting Systems Stadium.
Tom Allan netted from close range to put Brid Town ahead inside 20 minutes and almost doubled their advantage soon after.
Visitors Consett then levelled.
The Seasiders went back in front before the break as Joe Batty clipped home.
However, the second period belonged to the Tynesiders who levelled just before the hour.
Within ten minutes, they were in front for the first time then leapt on a defensive error to make it 4-2.
The visitors had a man sent off, 11 minutes from time, with Casey Stewart smashing in a last-gasp consolation right at the end.
Brid Town TV spoke to boss Scott Kerr post-match:


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