But on the third occasion it was the Stars who secured all the points.
Dundee took an early home advantage when they grabbed a powerplay goal at 3.05, thanks to Charlie Combs and assists from Michael Poirier and Dillon Lawrence.
Combs added another powerplay goal at 10 minutes exactly, with an assist from Phillippe Sanche.
Needing a positive reply in the second period the Giants pulled back a powerplay goal at 28.18 in the second period, with the Stars’ Timi Lahtinen in the box for slashing, when Jordan Boucher supplied David Goodwin and he made sure to slot the puck past Adam Morrison.
The sides were on equal terms when Sam Ruopp found the back of the net with 3.56 left in the middle period.
Despite early powerplays to both sides in the third period, neither was able to make the advantage pay.
At 43.21 Giants’ Goodwin was called for cross-checking, while at 47.58 Kyle Haas was sent to the sin bin for two minutes for delay of game.
Then at 57.48 the Stars’ went 3-2 in front with a goal from Lahtinen.
With the Giants pushing for the equaliser Jackson Whistle was pulled from Belfast’s goal leaving it empty.
Up stepped Dillon to score unassisted and to leave the game 4-2 to the home side.
Speaking after the game Belfast Giants head coach Adam Keefe said: “I thought that we had a slow start to the game, which was followed by five penalties and then going down 2-0. So we were obviously chasing the game from then on.
“I did like our push back and that is something that we can take out of the game. We also had a big powerplay goal ourselves and then another goal to tie the game up.”
Keefe believes that fatigue played it part in the Giants loss.
He explained: “We had a little bit of fatigue through the third period and we made some decisions that we should not have been making with the puck.
“I thought we controlled the majority of the third period but if you don’t score and you start forcing things we then got a little fatigued and we made some mistakes.”
Keefe concluded: “All in all we started the game slow and lost the special teams battle. But we are going to need to be much better next weekend.”
Keefe added that the Stars’ netminder Morrison had played superb games at the weekend against the Giants.
He said: “I can’t fault our guys for their efforts. Morrison played very well tonight as he also did in Belfast when we beat them. But we started forcing shots, forcing the puck into the middle and all of the sudden Dundee were able to skate and from that they got a bit of momentum. Then we make a mistake in our fore-check and the puck ends up in the back of the net. That’s the way it goes sometimes.
“We have certainly learned some lessons tonight against the Stars. We need to take those lessons into the following week games.”
With another tough week ahead of them Keefe believes that his side needs some time to recover.
He said: “Obviously we need to recover. I think we are down to nine and five right now. We need recover and get the legs back. I had thought even in the game at home in Belfast we were a little tired in the second half of the game and for portions of this game I also thought that we had looked tired. We need to recover and then go again next weekend, it’s that simple.”