After Australia declared at 465 for 8, Hampshire made 71 for 2 before bad light stopped play inside the last hour. They are still 238 runs behind.
Jason Gillespie, back from injury, took both wickets including that of the former Australian opener Matthew Hayden who was bowled for two.
It was a timely return to form by Waugh after he had managed just one half-century in his nine previous first-class innings. He hit 22 boundaries and three sixes off an ordinary Hampshire attack missing two of its front- line bowlers through injury.
He provided the backbone of Australia's innings and shared a 195-run stand for the third wicket with Taylor and then an 83-run fifth-wicket partnership with Michael Bevan (24).
Taylor, having scratched around for three hours on Saturday to reach 87, showed signs of returning to his best form.
While the form of Taylor and Waugh would have been a relief for the selectors, Steve Waugh (11) and Bevan again failed to put together decent score.
Shane Warne made hay at the end with two sixes and four fours in his 27-ball innings of 38.Reuse content