It was the first defeat at Huish Park for the Glovers since the return of manager Gary Johnson as they paid the penalty for wasting chances, particularly early on.
In the first minute top scorer Andy Williams fired over with only the goalkeeper to beat and a few minutes later Lawson D'Ath was clean through but Scott Flinders made a superb save.
Yeovil continued to press but Andy Williams was out of touch with his shooting. However, he did test Flinders just before the break with a low shot that the keeper saved well.
Hartlepool created only one clear first-half chance, substitute Ritchie Humphreys fired just wide as half-time approached.
The visitors snatched the win after 65 minutes. Defender Jonathan Grounds got his head to a left-wing free-kick as he attempted to clear but Noble, on loan from Sunderland, reacted quickly to hammer the winner past Sam Walker from close range.