Ayr looked the more determined side after the break and it was no surprise when after 59 minutes a well-struck volley from Tarrant took a slight deflection beyond Andy Goram to put Ayr in the lead at 4-3.
Tottenham almost drew level before halftime but winger Gareth Bale's powerful shot was well saved by David De Gea, after it had taken a slight deflection off defender Rio Ferdinand.