The pair have mustered only five goals between them since joining the club last summer but impressive strikes either side of the break sent Neil Lennon's side into Sunday's final.
Celtic, who will play the winner of Friday's tie between Ajax and Galatasaray, have postponed this weekend's Scottish Premiership clash with Kilmarnock to take part in the winter tournament.
They had started strongly, winger James Forrest causing problems, before Derk Boerrigter had a header cleared off the line.
Pukki made the pressure count in the 32nd minute when he fired into the far corner from 18 yards and Lennon's side were helped by a familiar face five minutes later when former Dunfermline and Hibernian defender Sol Bamba diverted Emilio Izagguire's cross into his own net.
Emre Gural pulled one back before half-time, when Lennon brought on Joe Ledley, Charlie Mulgrew and Kris Commons, but Celtic continued to dominate.
Balde struck a glorious third for the Scottish champions in the 57th minute, lashing into the top corner from 20 yards.
The game fizzled out as both managers shuffled their packs but Celtic finished convincing winners.