Adam Mackenzie top scored with six goals as Inverleith began their defence of the Scottish indoor title.
Former Olympian Stephen Dick and Patrick Christie also ended with three goals each from the games.
They lost 8-4 to Bromac Kelburne after being 4-0 down at half-time. They beat Grange 8-5 after being 4-1 ahead at the break and finished with a 3-2 victory over last season’s runners-up Grove Menzieshill.
Coach Stuart Neave said: “We were disappointed to lose the first game however we did not deserve it as we did not take our chances. We improved as the day went on and put in an immense performance against Menzieshill with a relatively small squad of players, eight of whom were playing at this level for the first time.
“Overall I am pleased with the day and happy in the knowledge that there is more to come.”