Betsy, making his first start following two substitute appearances for Pools on loan from Barnsley, fired into the top right corner after sidestepping defender Nat Clarke on 68 minutes.
Soon after Huddersfield's backline failed to pick up Mark Tinkler's run from deep with Adam Boyd swinging over a pinpoint cross for the unmarked midfielder to score with ease.
Boyd supplied the ammunition for Betsy's opener with another devilish centre and would have been on the scoresheet in the first half but for a superb reflex save by Phil Senior.
Youngster Senior, in the side as a cover for hand injury victim Ian Gray, blocked Boyd's powerful point-blank effort on 29 minutes.
Unmarked, Boyd seemed certain to score at will after Eifion Williams crossed from the left .
But Senior made a miraculous block and it looked like it was not to be Hartlepool's night when three minutes later Betsy beat Senior with a near-post header from Hugh Robertson's corner, only for Chris Brandon and David Mirfin to come to the rescue in a goalmouth scramble.
At the other end the Terriers created plenty of chances but failed to trouble Jim Provett's goal until midway through the second half.
Veteren striker Andy Booth was perhaps the most guilty party when he fired wide early on when a lay-off might have found any one of three Huddersfield players queuing up for a tap-in.
After the break Junior Mendes was presented with a free header from Rob Edwards' cross on 58 minutes, but despite seeming to have all the time in the world he somehow sent a close-range header careering over the bar.
The misses proved costly minutes later when Hartlepool's luck in front of goal changed and they could have added to their tally in the latter stages.