Police said it happened near a garden centre at Rogers Farm on the A24 near Findon, West Sussex.
The 79-year-old victim died at the scene, at about 20:40 BST on Thursday. A murder investigation is under way.
The suspect, described as a tall, skinny, white man in his 30s, is thought to have been driving the car in front of the man who was stabbed.
The attacker is said to have shoulder-length, wavy brown hair and was thought to be driving a pale "old-style" car.
It is believed the victim was travelling alone and that he was stabbed more than once.
Det Ch Insp Karen Mizzi said: "Officers have been urgently making inquiries overnight to trace the suspect.
"We need to hear from witnesses who saw the collision, the suspect or the car involved, particularly if anyone filmed the incident or saw anyone filming it."
Laura Muchmore, 21, who works in the garden centre close to the scene of the stabbing, said: "It's especially shocking that the victim was an old man.
"Findon is a really lovely little village. It's so picturesque and it's not known for this type of crime."
Edmund King, president of the AA, described it as a "horrific and tragic incident".
He said: "Thankfully, such brutal 'road rage' attacks are generally a rare occurrence on our highways.
"It appears that some drivers do react differently when they are behind the wheel than they would if they were walking down the street.
"They almost feel that the car empowers them but in reality it does not."

It will bring together British, Irish and German naval representatives, along with 200 descendants of those killed.
The event is being held on the centenary of the Battle of Jutland, the biggest and deadliest sea battle of the war, when 6,000 men in the Royal Navy were killed - 358 were Irish.
The commemoration will take place on HMS Caroline.
It is the only remaining ship from the 1916 battle off the coast of Denmark.
The battle was fought between 31 May and 1 June 1916 and involved about 250 ships.
It saw the Royal Navy's Grand Fleet, based at Scapa Flow in Orkney, clash with the German High Seas Fleet.
The centenary of the battle will be marked in Scotland, where a service in Orkney will be attended by German President Joachim Gauck along with the Princess Royal.
Representatives of all the nations connected to the battle, including Ireland, will attend that service.
A service of remembrance will also take place on board HMS Duncan at Jutland Bank, the site of the battle.
There will be a live stream of the ceremony on the BBC News NI website from 12:20 BST on Tuesday.
A manhunt is under way for a driver who stabbed another motorist to death after a collision between their two cars.
[NEXT_CONCEPT]
Belfast is to host a special all-island commemoration for Irish sailors who died in World War One.