Arthur Ashe hit 28 aces against Okker in the 1968 US Open final actually, including 16 in the first set, as I previously mentioned.
IIRC, Ashe served 37 aces once in a Slam final.
It was in a semi.
37 - Arthur Ashe (Australian Championship, now Australian Open 1967) 4 sets, defeated John Newcombe
37 - Tony Trabert (Forest Hills pro 1957) 5 sets, lost to Pancho Segura
30 - Josef Brabenec (Davis Cup 1979) 4 sets, defeated John Antonas (It wasn't a rubber from the World Group though: Canada vs West Indies; North American Zone)
30 - Michael Tauson (Davis Cup 1988) 4 sets, defeated Emilio Sanchez
Edit: forgot to mention this one:
46 - Ham Richardson (Forest Hills) 5 sets, defeated Ed Kauder (Kauder 59 ace performance has been mentioned here: Most aces hit in a match (more than 30)
+ 32 DF for Richardson which seems to be a record - 25 for Kauder.
Which means 105 aces in the same match.