The 25-year-old put the away side ahead when he took advantage of hesitation in the Silkmen's defence to score.
Paul Turnbull's cross from the right was turned in by Kristian Dennis, as the hosts levelled before half-time.
However, Blissett restored the Gulls' lead early in the second half, as he headed in Danny Racchi's precise corner for what proved to be the winner.
Victory leaves Torquay five points adrift of safety.
Nathan Blissett's double helped relegation-threatened Torquay pull off a surprise win away at Macclesfield.