Gardaí called out to customers, including mothers with their children, in the Citywest Shopping Centre to “get down, get down” as they pursued the man, arresting him as he emerged from an exit.
A firearm, believed to be a loaded submachine gun, was recovered from the man as six officers managed to restrain him and take him into custody.
The 37-year-old criminal had earlier carried out an aggravated burglary, in which he bashed a man in the head with the butt of the gun, and later pointed the weapon at another man.
He was being questioned last night and is expected to be brought before court to face serious charges.
The man has multiple convictions in Ireland and Britain, for violent robberies and carjackings, as well as a petrol bomb attack.
His arrest marked the end of a terrifying ordeal which began at 6.20am, when he attacked his partner at her home in Brookfield, west Tallaght, and stole her car.
He crashed her car a short distance away on Russell Square in nearby Jobstown.
There, he carjacked another vehicle and it is thought he drove down onto the N81, abandoning it soon after on Whitestown Way, near the Tallaght Stadium.
He walked a short distance behind the Sean Walsh Park into Watergate Estate, in the Old Bawn area. There he kicked in the door of a house and carried out an aggravated burglary.
A man was in the house at the time along with his daughter and her child.
It is understood the man went to the front door and that during a confrontation, the burglar kicked in the glass panel of a porch and forced entry.
He struck the owner in the forehead with the butt of his gun.
The burglar took the man’s 162-reg black Renault Kadjar.
Senior officers in Tallaght scrambled all units and called in the Armed Support Unit, the Emergency Response Unit as well as the Air Support Unit.
They assisted local uniform and detective officers in piecing together the man’s movements.
He was later spotted on the Ninth Lock Road in Clondalkin, some 8km north of Watergate Estate.
At some stage, he abandoned that Renault Kadjar at a restaurant on the Naas Road and hijacked a Volvo.
He then abandoned that vehicle at a car showroom, pointed the gun at the salesman and stole a Subaru Impreza.
He later transferred from this car to a Mercedes E-Class.
Garda units pursued him into Citywest, west Tallaght, where he was forced to abandon his car and fled into Citywest Shopping Centre.
He was chased and arrested shortly after 2pm when he emerged from one of the exits.
He was taken to Tallaght Garda Station and detained under Section 30 of the Offences Against the State Act. He can be held for up to 72 hours.
Garda Representative Association president Ciaran O’Neill said: “Well done to those colleagues in the apprehension of an armed man in Tallaght. Just shows the dangers we face every time we go into work.”
Local Fianna Fáil TD and spokesperson for Dublin, John Lahart TD, said: “I commend the work of each the members of An Garda Síochana that were involved in [the] successful operation. I am relieved that there was no loss of life or major injury and that the armed suspect involved is now in Garda custody.”