Browne's try helps Hinch grab a vital win
It wasn't a great return for Ulster's three representatives in Division 1B as only Ballynahinch managed to come out of the weekend with the intended result.
Which meant that Banbridge had their first taste of defeat - to the tune of 33-14 this term - after having racked up four wins and a draw prior to visiting leaders Shannon.
And Ballymena succumbed to a fourth loss after six rounds of games but by the slimmest of margins with UCC winning 35-34 at Eaton Park.
The Braidmen did, at least, walk away with two valuable points due to managing four tries in addition to their losing bonus point.
Hinch's determination to put the previous weekend's defeat at Banbridge behind them paid off at Ballymacarn Park where they beat Naas 18-10 and swapped places with Bann to go back to second in the table.
Not that it was a wholly convincing return to winning ways for Brian McLaughlin's squad as only Aaron Cairns's last-gasp penalty - a week after starting for the first time for Ulster - gave the Co Down side some breathing space and also denied the visitors a losing bonus point.
They had trailed 10-8 at the break following David Busby's first-half try, which came from a high ball launched by out-half James McBriar, and Richard Reaney's penalty.
And it was only after the hour mark when Ulster player Pete Browne drove over for a try, in the wake of a Callum McLaughlin break, did they snatch the lead again.
Cairns's conversion put them 15-10 up and how it stayed, with Hinch's defence working well against several surges from the visitors, until the home side's scrum-half nailed his 80th-minute strike from the tee.
Hinch now go on to face what is sure to be a no-quarter given Ulster derby at Ballymena which is scheduled for Friday night at Eaton Park.
Down in Limerick, Bann were never really in a game with Shannon who led 21-7 at the turnaround and the league leaders went on to nail their bonus point try in the second half before rounding things off with a fifth touchdown.
Dan Soper's squad, with prop Michael Cromie making his 100th AIL appearance, managed just two tries in what was a deeply disappointing outcome.
Second row Robin Sinton got their first in the opening half before number eight Stevie Irvine carried the ball over the Shannon line in the second half with Ulster squad member Rob Lyttle converting both.
As for Ballymena, they found themselves having to find a way back against UCC with the scoreboard reading 35-20 in favour of the Cork students.
The first half had been a similar story for coach Andy Graham's squad as they trailed 15-6 before the half hour was up.
Centre Angus Kernohan then managed to make his way over the UCC line for Ulster squad player Brett Herron - who ended the day accumulating 19 points - to add the conversion which cut the visiting side's lead to 15-13 at the break.
The Braidmen then snatched the lead following hooker James Taggart's try which was again converted by Herron.
But it didn't last and lock Conor Smyth's yellow card proved very costly before the Braidmen - trailing 35-20 - finished with a strong surge and converted tries from Smyth and Herron which just saw them finish short.
Results: Division 1B: Ballymena 34 UCC 35, Ballynahinch 18 Naas 10, Old Belvedere 18 UL Bohs 13, Old Wesley 34 Dolphin 5, Shannon 33 Banbridge 14