Thornton struck twice in the first half, either side of Korey Smith's leveller, as Orient claimed only their second victory in 14 games to pull four points clear of the drop zone.
Orient went ahead three minutes into an absorbing first half when Thornton, back from a two game suspension, latched onto a Scott McGleish header and punished some uncertain City defending.
Norwich equalised after 20 minutes when Smith rounded off a neat passing move with a drive from just inside the area.
But Thornton restored Orient's lead on the half hour with a far-post header from Charlie Daniels' free-kick.
Daniels almost added a third for Orient following a fine run from the halfway line, while at the other end Jamie Jones pushed away a fierce drive from Canaries substitute Stephen Hughes.
Hughes hit the bar in stoppage time, but Orient held on to record their first victory under new manager Russell Slade.