Melbourne Cup fervour got the better of two people arrested by police on Tuesday – a young drunk bleeding from a facial wound and a drink-driving septuagenarian.

But other than that sore and sorry pair emergency services say the Cup crowd was largely well-behaved this year.

Police are investigating allegations a punter was head-butted by a security guard near Flemington's betting ring on Tuesday afternoon.

The young man appeared to be bleeding from the head in the aftermath of the incident. He was treated by paramedics before he himself was arrested by police for being drunk.

Police also arrested a 75-year-old Hastings woman after she was spotted driving the wrong way around a roundabout as she tried to get home from a race day function at her favourite bowls club in Hastings about 5pm.

A concerned motorist called police. When they flagged her down she recorded a blood alcohol reading of 0.122 per cent.

The woman was fined $661 and her licence was immediately cancelled, a police spokesman said.

Police arrested nine people at the racecourse on Tuesday, seven for drunkenness, one for assault and one for drug trafficking. Police and security staff evicted 78 people over the course of the day.

Other than those incidences, a police spokesman said the 97,479 that gathered at Flemington for the Cup behaved themselves quite well.

Paramedics treated 31 people at the track on Tuesday. Five people had to be taken to hospital, but those were mainly medical incidents rather than alcohol-inflicted injuries, a spokesman told Fairfax Media.

Those numbers were slightly down on 2015, the spokesman said.