Malta, who have not won a match since beating Estonia four years ago, gamely packed their defence and held out for the opening 15 minutes.
After sustained home pressure the first goal arrived when Mark Kinsella's corner was flicked on in the six-yard box. Robbie Keane was first to react and he jabbed it over the line to become the Republic's youngest goalscorer, at 18 years and three months, since Johnny Giles against Denmark in 1959.
The Wolves forward doubled his tally two minutes later with a solo run through the middle and a perfectly placed shot beyond the visitors' goalkeeper, Reggie Cini.
Malta were hardly able to get out of their own half, such was the gap in class. It was a major surprise when they had their first shot of the game, a speculative 25-yard effort by David Carabott which flew well wide.
It should have been 3-0 when Quinn latched on to Kinsella's right-wing cross inside the six-yard box and turned to hammer it at goal, only to see the 38-year-old Cini somehow divert it around a post for a corner.
The third Irish goal arrived in the 53rd minute and the name on the scoresheet was again Keane - but this time the marksman was their captain. After the hard-pressed Maltese defence cleared the danger, the ball rolled into Roy Keane's path 30 yards out and his low shot was fumbled over the line by Cini.
Quinn added Ireland's fourth goal in the 63rd minute - his 17th for his country but his first at international level for more than two years. From Damien Duff's low cross from the left, the big Sunderland striker glided his side-footed shot out of the goalkeeper's reach.
The Coventry defender Gary Breen was next on the list for the Irish, strolling around Cini and planting the ball in an empty net in the 82nd minute.
REPUBLIC OF IRELAND: Given (Newcastle); Kenna (Blackburn), Staunton (Liverpool), Breen (Coventry), Cunningham (Wimbledon), Roy Keane (Manchester Utd), McAteer (Liverpool), Kinsella (Charlton), Quinn (Sunderland), Robbie Keane (Wolves), Duff (Blackburn). Substitutes: Cascarino (Nancy) for Quinn, 74; Kennedy (Wimbledon) for Robbie Keane, 83; Carsley (Derby) for McAteer, 84.
MALTA: Cini (Valletta); Sixsmith (Naxxar Lions), Chetcuti (Valletta), Spiteri (Hibernians), Debono (Naxxar Lions), Buttigieg (Floriana), Turner (Sliema Wanderers), Carabott (Hibernians), Suda (Birkirkara), Brincat (Birkirkara), Zahra (Birkirkara). Substitutes: Agius (Valletta) for Suda, 66, Zammit (Birkirkara) for Zahra, 70, Camilleri (Hamrun Spartans) for Sixsmith, 77.
Referee: R Olsen (Norway).