But seven from a possible eight has given the team hope as it battles for eighth spot - the last play-off place.
Defenceman Kyle Thacker marked his home debut with the opening goal while the club’s other new recruit, veteran Chris Lawrence, was a key figure all night long, and an easy spot for MoM.
Jeff Hutchins, assistant coach, pinpointed the growing confidence among the players as key to a late push to get out of last place in the EIHL.
Flyers now trail ninth-placed Dundee Stars six points, and eighth placed Glasgow Clan by seven.
Their Scottish rivals both have games in hand, but head to head meetings at the end of this month could hold the key to the season.
Hutchins said: “Confidence is a huge thing. We have played with the lead the last four games, and that goes a long way to setting us up for rest of the game.”
Flyers were certainly a match for Giants in a game that remained scoreless for over half an hour.
A fifth minute strike from Kristian Blumenschein was washed off after a video review, while Giants saw a golden chance go begging after Tyler Soy waltzed through the defence only to take a tumble off his skates as he went for goal.
In the second period, Giants; netminder Jackson Whistle pulled off a fine save to deny Brandon Magee, while David Goodwin missed a gilt-edged chance at the back door with a shot which barely troubled Shane Owen.
The deadlock was finally broken after 32 minutes when Thacker took a fine pass from Carson Stadnyk and rifled the puck into the net.
Giants responded, netting just four seconds into a powerplay through Goodwin to send the teams into the second break at 1-1.
Flyers struck on the powerplay just 1:05 into the third as Lawrence netted the rebound from a Blumenschein shot, and they held that advantage until the closing two minutes.
Giants kept the pressure up, and it finally paid off when Slater Doggett rang the red light to take this match into sudden death overtime.
That failed to deliver a winner, and it was on to penalty shots with Goodwin netting and then Tommi Jokinen’s miss sealing victory for the visitors.