The 53-lap race was won by David Coulthard driving for McLaren after starting from sixth position on the grid.
The Ferraris of Michael Schumacher and Eddie Irvine qualified ninth and tenth respectively.
At the start Alesi led with Frentzen in second and Coulthard moving from sixth on the grid into third place.
The top six after Häkkinen's puncture was Coulthard first, Alesi second, Frentzen third, Fisichella fourth, Villeneuve fifth and Michael Schumacher in sixth.
David Coulthard dedicated his win in this race to Princess Diana, who had been killed in a road accident the week before.