Replacements: Aaron Ferris, Richie Lobb, Neil Faloon, Matthew Nelson, Michael Cromie.
Replacements: Kieran Moloney, Risteard Byrne, Adam Clarkin, Shane O'Meara, James Thornton.
However, Derek Suffern's men look destined to face a relegation play-off against Buccaneers, the second-placed team in Division 1B, as Dolphin and Young Munster are four and five points ahead of them in the table respectively entering the final round.
The conditions were almost perfect for Ballynahinch's final home league game of the season. A firm pitch was bathed in sunshine with a strong breeze bowing diagonally towards the clubhouse end.
Playing into the breeze towards Slieve Croob in the first half, Suffern's side made the perfect start.
Centre and captain Morrow set off on a counter attack in the fifth minute but was quickly closed down. His pass inside went to ground but was snapped up at pace by McBurney and the 'Hinch full-back raced clear.
McBurney twisted and turned and when he reached the UCD 22, stepped past his opposite number Niall Earls to run in and dive over behind the posts for a dramatic opening score. Ulster's David McIlwaine added the conversion.
'Hinch's lead did not last long however, with UCD wasting little time in getting back into 'Hinch territory as out-half Liam Bourke kicked with great accuracy.
The visitors' pack started to take the ball through a number of phases and then scrum half Jamie Glynn released it wide. 'Hinch out-half Harry McAleese had drifted too wide in defence, providing UCD centre Kelly with a massive gap to shoot through and touch down behind the posts. The extras were supplied by Earls.
Ballynahinch had the better of the exchanges for the next 20 minutes. McIlwaine missed a long range penalty attempt and when the hosts were awarded three further penalties, they signalled their intention to score tries when they opted to scrum or kick for the corner.
The UCD defence was strong and well organised and despite these long periods of pressure, the'Hinch attack failed to capitalise on their hard-earned field position.
As the first half drew to a close College won a penalty on halfway and sent the ball deep into the left corner. The lineout was secured and play was flashed across the 'Hinch 22.
At the first ruck the home defence was slow to react with on pillar in position on the openside of the breakdown. Hooker Tracy was quick to spot the opportunity, picking up and running clean through to score. Earls' simple conversion made it 14-7 for half-time.
'Hinch started the second half with a bang, playing with a lot more tempo and energy. After a number of phases, Aaron Cairns found his skipper Morrow at pace and the big centre did well to smash his way over to score. McIlwaine's conversion was on target for a 14-14 scoreline.
The home side then took the lead in the 58th minute when McIlwaine landed a penalty from distance after a UCD ruck infringement.
From the restart, McAleese and Cairns used the wind well and the College back-three of Earls, Paddy Dix and Billy Dardis had a busy afternoon.
The star of the Hinch pack was flanker Paul Pritchard, his work on the ground was really impressive as he won countless turnovers or forced the students to concede penalties.
Following a Pritchard steal in the 64th minute, the 'Hinch pack took play to underneath the College posts. The visitors conceded another penalty, this time replacement Adam Clarkin was caught pulling the ball back with his hands in a ruck and referee Leo Colgan issued a yellow card.
Ballynahinch opted to scrum and after a series of resets, the home pack managed to gain enough ground to allow number 8 Graham to pick up and score beside the posts. McIlwaine converted to take 'Hinch 24-14 clear.
With UCD down to 14 men, the County Down outfit pushed hard for the bonus point try. They had numerous chances to score but all credit to the students' sheer determination, they managed to keep the home side out.
But that fourth try eventually came in the 77th minute after impressive scrum half Cairns had gone close following a long period of sustained pressure.
The 'Hinch pack quickly secured the ball again with Graham picking up to reach over the line. Referee Colgan had a long look before awarding the try. McIlwaine had his conversion attempt charged down by Dix.
It was another excellent result for resurgent Ballynahinch who will have to do it all again next Saturday as they make the trip south to Dublin to play Clontarf, who are second in the table and fighting Old Belvedere for the league title.
If 'Hinch could make it four bonus point wins in-a-row - along with the results involving the two teams above them, Dolphin and Young Munster, going their way - it would prove to be a remarkable comeback at the end of what had been a very tough season.
"We have done nothing different from what we have been doing since the start of the year," admitted Suffern after the UCD game.
"I suppose it has taken that long for us to realise how we need to play in this league from a confidence point of view. Now we are confident, we are doing really well and we can compete with any team.
"I think confidence is a massive thing. It is just about winning, you get into a bit of habit as we well know from previous years. I suppose when you lose games early and you are up a division, then ship a few injuries that confidence goes.
"Certainly over the last three weeks we have been very, very good. We have stuck to our patterns of play and it had paid dividends, the boys have shown great character - working hard every Tuesday and Thursday - and now it is eventually reaping some rewards."
He added: "We are at Clontarf for our last game and I believe if we are close at half-time we can maybe get something out of the game.
"If we could go down there and get a win and get the five points...well you just never know the way results go at this time of year, we might just get out of that play-off spot yet."
Referee: Leo Colgan (IRFU)