Goals in the first 20 minutes by Robbie Keane and Gary Breen saw the Irish off to a brilliant start, but the Malta full-back Brian Said chipped the Irish goalkeeper, Alan Kelly, to reduce the Group Eight rivals' arrears in the 61st minute and David Carabott converted a penalty for the equaliser seven minutes later.
It was left to Staunton to revive the faltering Irish with his wonderful strike from 25 yards after Niall Quinn had been fouled.
The Republic had started their third European Championship qualifier in eight days in sparkling fashion, fully justifying Mick McCarthy's decision to revert to the attacking line-up which had produced the 2-1 defeat of Yugoslavia a week ago.
It was Quinn who set up the opening goal in the 13th minute for his strike partner, Keane, with a perfect pass that sent in the Coventry City striker unmarked for a clinical finish from 15 yards.
The second goal came eight minutes later when Breen found himself unmarked to crack a cross from Kevin Kilbane firmly past the helpless Ernie Barry.
More than 5,000 travelling Irish fans turned Malta's Ta'Qali Stadium into a mini Lansdowne Road and, with fond memories of former manager Jack Charlton's team clinching World Cup 1990 qualification here, at that stage they believed another step had been taken towards a place in next summer's finals.
Quinn had used his power in in the air right from the start, but it was his snap-shot in the seventh minute from a Mark Kennedy cutback which brought the first corner when it deflected off the Malta sweeper, John Buttigieg, a former Brentford player.
Keane, terrorising the Malta defence with his elusive pace, had another chance six minutes later when fed by Kilbane after Breen broke up a Malta attack on the halfway line. This time his shot was blocked by Barry.
Gallant Malta tried to hit back and Carmel Busuttil struck a powerful drive from 20 yards, but Alan Kelly flung himself to his right and turned the ball away for a corner. Shortly afterwards, the Maltese lost their influential midfielder, Jeffrey Chetcuti, through injury.
Ireland were soon piling into the islanders again and Keane had a goalbound 25-yard shot blocked, Kinsella's follow-up being well held by Barry.
The Maltese suffered another blow on the half hour as Buttigieg was forced off by injury to be replaced by Silvio Vella.
Only a goalline clearance by Gilbert Aguis, the striker back helping his hard-pressed defence, prevented Quinn's header from a Staunton cross producing a third Irish goal in the 35th minute.
Malta looked better when Aguis, Busuttil and Chucks Nwoko combined in an attractive move and the naturalised Nigerian, Nwoko, fired marginally wide.
Staunton prevented Malta pulling a goal back four minutes after the break, heading Camilleri's bullet free-kick off the goalline.
It sparked a spell of pressure by the hosts, but Ireland could easily have gone further ahead three minutes later when Quinn's close-range diving header went just wide from a Steve Carr cross.
MALTA: Barry (Sliema Wanderers), Said (Floriana), Chetcuti (Valletta), Carabott (Hibernians), Debono (Valletta), Buttigieg (Floriana), Busuttil (Sliema Wanderers), Saliba (Valletta), Nwoko (Birkirkara), Camilleri (Sliema Wanderers), Agius (Valletta). Substitutes: Muscat (Hibernians); Vella (Hibernians), Spiteri (Hibernians), Sultana (Hibernians), Okonkwo (Naxxar Lions), Mifsud (Rabat Ajax), Buhagiar (Floriana).
REPUBLIC OF IRELAND: A Kelly (Blackburn), Carr (Tottenham), Staunton (Liverpool), Breen (Coventry), Cunningham (Wimbledon), Carsley (Blackburn), Kilbane (West Bromwich), Kinsella (Charlton), Quinn (Sunderland), Robbie Keane (Coventry), Kennedy (Manchester City). Substitutes: Kiely (Charlton); Cascarino (Nancy), Connolly (Feyenoord), Duff (Blackburn), McLoughlin (Portsmouth), G Kelly (Leeds), Harte (Leeds).
Referee: S Capodban (Romania).Reuse content