Fu fought back from 2-0 down for parity heading into the mid-session interval after almost two hours of play before a superb 142 total clearance gave him the lead for the first time in the match at 4-3.
A second century of 110 put him 5-4 up before the Hong Kong player came from behind to snatch the 10th and reach another ranking event final just after midnight local time in Germany.
Another Englishman stands between Fu and the title, as Carter overcame Neil Robertson 6-2 in the other semi. The two will decide the 2013 champion on Sunday.
Though Hawkins' 41 break was one short of Fu's opening frame-effort of 42, it was followed up with some deft safety play to create an opening for the steal and 1-0.
The world number 17 doubled his advantage after a near hour-long battle of snookers and counter-snookers which saw Fu miss a simple final brown and gift Hawkins the chance to prevent his opponent returning the fightback favour.
Hawkins was unable to register a single pot in the third frame, however, as three mini-breaks helped Fu pull one back before a 68 break from the Hong Kong potter meant the two were back on level terms at the interval.
Australian Open champion Hawkins re-took the lead with his only half-century of the match, a 58, but the world number 23 Fu again used tight cueing and cautious shot selection to edge his way to 3-3.
And Fu picked the perfect time to step his play up another level as his pinpoint accuracy led to a near-perfect 142 head-to-toe break to finally take the lead for the first time in the semi-final.
Though the lead didn't last long, Fu would regain the advantage with a 110 and after seemingly blowing a chance to avoid a deciding frame, Hawkins allowed the 35-year-old back in to finish the job and move one win away from glory in the first ranking event of 2013.
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