Adrian Nadasan, 45, was driving in a “dangerous” manner in Wisbech, magistrates in Peterborough were told on Monday.
Prosecutor Peace Egbulefu said: “He was driving at speed and suddenly braking, narrowly avoiding a collision with the police vehicle.
“When the officers spoke to him he had glazed eyes and had very slow reactions and responses to questions put to him.”
Nadasan, of Orange Grove, Wisbech, was arrested on suspicion of drink-driving.
In custody he blew 82 microgrammes of alcohol in 100 millilitres of breath, the legal limit being 35.
The defendant, who had no previous convictions, pleaded guilty to drink-driving.
Kashif Khan, mitigating, said Nadasan had been drinking after splitting with his partner of four years.
The solicitor added: “He was depressed and he tried to drown those feelings by drinking before he was stopped by the police.
“He’s embarrassed by his behaviour and he would like the court to be aware that this was a one-off incident which will never happen again.”
Nadasan was banned from driving for 20 months, which can be cut by 20 weeks with completion of a drink-driver rehabilitation course.
He was also fined £280 and ordered to pay £139 in costs and victim surcharge.