Dalton, 18, a second-half substitute, latched on to Andrew Wright's perfectly judged cross to put Blyth into the third round of the FA Cup for the fourth time in their history.
The home side had the best of the early exchanges with skipper Gareth Williams peppering visiting goalkeeper Shwan Jalal with some high balls. But the former Tottenham keeper stood firm and it was the Cherries who had the first sight of goal but Lee Bradbury's 20th-minute strike failed to trouble Mark Bell in the Blyth goal.
The game turned on its head early in the second half when substitute Brett Pitman was given a straight red card after a late challenge on Paul Watson. The 20-year-old received his marching orders for a late challenge from behind on Watson just three minutes after coming on.
The home side almost took advantage immediately but after smart work from Shaun Reay - Blyth's two-goal hero from the first-round win at Shrewsbury - Robert Dale curled a shot wide. But Spartans were not to be denied, and when fellow substitute Wright got clear down the left, Dalton was on hand to send the 4,200 home fans wild.