Neither Nakamura, 27, who became the first Japanese player in the SPL, nor Maloney, 22, a Scotland Under-21 international, are physically imposing. But Nakamura is a bundle of tricks and Maloney a fleet-footed dynamo.
Nakamura was at the heart of the action against visitors who were sunk by John Hartson's composed first-half finish and Craig Beattie's third goal from the bench in three games.
Gordon Strachan said Nakamura was "as good as I've seen in a long, long time." The man himself was semi-satisfied. He nearly scored several times, most notably from a curling left-foot free-kick which was won with trickery.
Celtic's season started in turbulence. Now Far Eastern promise is revitalising Glasgow's east end.
Goals: Hartson (37) 1-0; Beattie (88) 2-0.
Celtic (4-1-2-1-2): Boruc; Telfer, Baldé, McManus, Camara; Lennon; Petrov, Thompson; Nakamura (Beattie, 84); Zurawski (Maloney, 64), Hartson. Substitutes not used: Marshall (gk), Aliadière, McGeady, Wallace, O'Dea.
Dundee United (4-5-1): Stillie; Wilson, McCracken, Archibald, Duff; Crawford, Kerr, Brebner, Robson (Samuel, 48), McIntyre; Miller. Substitutes not used: Dodds, Samson (gk), Kenneth, Holmes, Robertson, Cameron.
Referee: I Brines.
Booked: Celtic Petrov; Dundee United Crawford, McCracken.
Man of the match: Nakamura.