McGeady, who had failed to start since the opening-day 4-4 draw at Motherwell, sent out a reminder of his talent and he quickly made Celtic forget about the loss of Chris Sutton in the only change from the win at Dundee United.
The Republic of Ireland international winger's quick free-kick saw Maloney open the scoring and then they exchanged roles a minute later for McGeady to score before the young Scot played a part in Hartson's record goal.
Falkirk had to wait 18 minutes for their first chance when Steven Thomson drove Gow's knock-down wide from 20 yards out. But they were living dangerously at the back.
Maloney's quick thinking piled the misery on the home side when he slid the ball through the gap for Mo Camara down the left flank. The wing-back then fired low into the area and Maloney arrived to sweep the ball past Glennon from 10 yards. McGeady completed a stunning minute for Celtic when accepting Maloney's pass before sending the ball low into the Falkirk net from 11 yards.
Falkirk refused to lie down and Artur Boruc was tested by Darryl Duffy's 22-yard strike in the 49th minute. On the hour, however, Hartson's persistence got him behind the Falkirk defence but his weak shot was saved before Stilian Petrov fired over. Matt Glennon then did well to save Maloney's powerful shot but it fell to his strike partner to send the keeper the wrong way.
"There's better players than me who've never done that achievement at Celtic like [Jorge] Cadete, [Pierre] van Hooijdonk and [Paolo] di Canio," Hartson said. "So to join a list of other famous names who have done it makes me very proud."
Goals: Maloney (41) 0-1, McGeady (42) 0-2, Hartson (69) 0-3.
Falkirk: Glennon; Lawrie, Scally, Milne, Ireland, Latapy (McBreen, 70), Steven Thomson, Moutinho (Lima, 57), O'Donnell (O'Neil, 68), Gow, Duffy. Substitutes not used: Ferguson, McPherson, McStay, Twaddle.
Celtic: Boruc; Telfer, Camara, Baldé, McManus, Petrov (Pearson, 75), Lennon, Nakamura, McGeady, Maloney (Virgo, 83), Hartson (Wallace, 83). Substitutes not used: Marshall, Varga, Lawson, Agathe.
Referee: C Murray (Scotland).
Booked: Falkirk Duffy, Milne. Celtic Petrov.
Man of the match: Maloney.
* Hearts, who beat Dundee United 3-0 on Saturday, were yesterday refusing to be drawn on speculation linking Graham Rix with the managerial vacancy at Tynecastle. The former Chelsea first-team coach has emerged as a possible replacement for George Burley. Sir Bobby Robson insists he is also waiting on a call from majority shareholder Vladimir Romanov about the vacancy.Reuse content