Double world championship finalist Carter retrieved the two snookers he needed to give himself a chance to win the first frame, but Fu finally scrambled into the lead by holing a splendid long pink with the tension palpable already before almost two thousand German snooker fans.
A break of 55 earned the man from Happy Valley in Hong Kong a 2-0 lead before Carter won his first frame of the final with his own version of Fu's 55.
Carter was first among the balls in the fourth frame, but paid a heavy price for a glaring miss on a red using the rest as Fu returned to the table to piece together an imperious 104 for a 3-1 advantage.
Carter redoubled his efforts after the mid-session interval to draw level at 3-3.
A 70 was enough to win the fifth frame with Fu slipping up among the balls on 38 as the break concluded messily with what appeared to be a push shot.
Carter worked his way back into the frame with Fu missing a long red late in the frame that would ultimately cost him it.
As both men suddenly warmed to their respective tasks in the vast area, errors were being punished and Carter would watch Fu make 83 for a 4-3 advantage after an attempt to escape from a snooker left his opponent with plenty of balls to go at.
It seemed likely that it would go 4-4, but Carter somehow missed a cut on a red at the scoring end of the table after Fu had made a mess of potting an easy black off its spot.
Fu's 33 was enough to leave Carter needing a snooker, but this time there would be no late drama in trying to get them.
It might yet prove to be a pivotal moment in the final with the first man to nine frames claiming the trophy and cheque for 60,000 euros when they resume play at 7pm (GMT) this evening.