He then stopped, reversed and rammed the patrol car.
The defendant was banned from driving at the time.
Judge David McHugh described Smithers's driving escapades as 'madness' and sentenced him to six months in prison, banned him for 15 years and fined him €1,300.
The defendant, of Casement Drive in Finglas, admitted before Blanchardstown District Court to two counts of dangerous driving as well as charges of criminal damage, driving without insurance or a driving licence, and drunken driving.
The incident took place at Ratoath Avenue in Finglas on June 2 last year.
Garda Sergeant Maria Callaghan said gardai were on mobile patrol on Ratoath Road when they saw a green Nissan Micra driving at high speed.
Smithers crashed the car into an ESB pole, but took off when he saw the garda car.
He drove over a green area and completed a number of handbrake turns, then drove on the wrong side of the road along Ratoath Avenue.
Smithers stopped outside Kilshane Retirement home, then reversed the car and rammed the patrol car, causing €700 worth of damage.
He then drove off again but lost control and crashed.
He was arrested and taken to Finglas Garda Station where he provided a urine sample. It gave a reading of 373mg of alcohol per 100ml of urine.
The court heard Smithers has 73 previous convictions, including 12 previous convictions for driving without insurance. He was also serving a 25-year driving ban at the time.
Defence solicitor Mairead White said Smithers realised his behaviour was appalling and wished to apologise.
The defendant was on cocaine and tablets at the time and was drinking heavily.
The solicitor said Smithers, a father of two, has recently served a prison sentence and is now clean of drugs.
He hasn't been in trouble since this incident, and has linked in with addiction services in Finglas.