The home side made the brighter start to the match, and took the lead early on when Baptiste Laverroux capitslised on a well-crafted scissors move to beat the Reds defenders and score.
Scrum-half Owenson missed the conversion, but Musselburgh led 5-0.
However, the visitors struck back shortly after in sensational fashion when winger Calum Cockburn burst through a hole in the 'Burgh defence, beat the convering defender and grabbed his second try of the season.
Nick Bell, who had moved to scrum-half to accomodate the absence of injured Stuart Miller, kicked the resulting conversion and the Reds led 5-7.
However the hosts showed why they have been around the top of RBS Championship B all season with some clever interplay as half-time approached.
Lance Gahan was the beneficiary of clever Musselburgh handling, the full-back squeezing over at the corner for the home side's second try.
Owenson was again off-target from the tee, albeit from a difficult angle. (10-7)
The Reds' pack attempted to muscle their way into the game, with back-row duo Callum Champion and Colin Stuart to the fore alongside ever-present lock Ben Laing.
However, the home side struck again thanks to a brilliant dummy by stand-off Jye Thomas, which allowed Andy Lamb over under the posts. Owenson was this time on target to give Musselburgh a 17-7 lead.
Bryan Craig's side needed the next score, and it came from the boot of Bell.
The forwards made good ground, and 'Burgh were penalised at the breakdown, allowing Bell to add the three points.
Half-time: Musselburgh 17-10 Haddington
The hosts turned the screw shortly after the resumption and notched their bonus point try when Owenson's superb break was rounded off by openside Lamb.
The scrum-half had found his kicking boots and duly added the extras to make it 24-10 and leave the visitors a mountain to climb.
Owenson added another penalty to extend the hosts' lead before the Reds struck again.
Calum Cockburn was having a storming afternoon, and snatched a poorly placed 'Burgh kick before beating several defenders en route to the line. A solo special from the big winger.
Bell's conversion and a penalty shortly after meant the Reds were back in touch at 27-20 and it was 'game on' again at Stoneyhill.
Both sides then had a man sent to the sin-bin, as Callum Champion and Lance Gahan were sent for a breather.
However, the Reds pack were firmly on top by this stage and, from a well-worked line-out, shoved the Musselburgh pack over their line.
Ben Laing, the man who hadn't scored for three seasons, was credited with the try - his second in a few weeks.
Bell's extras meant it was 27-all and the scrum-half would have a bigger part to play towards the end.
He darted over for the Reds' fourth try late on to put the club in front, and duly converted his own try to set up a grandstand finish to the East Lothian derby.
However, victory was snatched from the visitors' grasp when Conor Slaven went over, allowing Owenson to tie the scores at 34-all.
The Musselburgh scrum-half then stepped up to kick the winning penalty, and deny the Reds a famous victory at Stoneyhill.
FINAL SCORE: Musselburgh 37-34 Haddington
A hugely disappointing finale to the East Lothian derby for Craig and his side, but they will take heart in the second-half performance as they prepare for the trip to face Aberdeenshire on Saturday.
pic courtesy Musselburgh RFC