The champions, who led on first innings and resumed yesterday's third and final day on 180-5, declared their second innings on 299-8, for an overall lead of 463 runs.
Paul Palmer, who was 53 not out overnight, went on to make an unbeaten 108, while Donovan Nelson, who top-scored with 62 not out in the first innings, chipped in with 41.
Port Antonio, batting a second time, then reached 98-4 with pacer Richard Simpson getting 2-24 and Nelson 2-22.
"We played some good cricket throughout the three days," said a delighted Clive Ledgister, coach of STETHS.
"We first managed to reach a good first innings total, with Nelson and Donaldson Gordon making huge contributions. When we bowled, MacKoy Ewart bowled a good line and length.
"We now look towards the Spalding Cup play-offs where, hopefully, we can go there and play our best game of the season," added Ledgister.
Port Antonio coach, Carl Brissett, said a bad first day cost them the match.
"We lost the match from the first day with a lot of dropped catches and mis-stumpings. We had them at 3-53 and 178-8 and let them off the hook. After that we were always playing catch up," explained Brissett.
"We plan to rebuild next year so I don't expect a great deal. But, come the next three years, we will be back. We only started playing Headley Cup five years ago where we won the (now defunct) Headley Cup 'B' League last year. So, despite not winning the big one, I think we have a lot to be proud of," he added.
STETHS will play Eltham High in the all-island Spalding Cup play-off later this month.
- Jermaine Lannaman