But the Australia leg-spinner had to watch his side overcome a middle-order collapse before they stumbled across the finish line.
Resuming on their Saturday score of 13 for two, after Sunday's total washout, Hampshire slumped to 52 for seven chasing a mere 109 for victory after Warne himself had taken five for 68 as Durham were dismissed for 201 in their second innings.
But Will Kendall (31 not out) and Dimitri Mascarenhas (33 not out) then shared an unbroken eighth-wicket stand of 60.
Durham pace bowler Liam Plunkett took four for 48 but it was not enough to force a victory for the visitors with Mascarenhas hitting the winning runs off West Indian fast bowler Reon King.
Afterwards, Warne told the BBC: "We showed great courage to bounce back after being in such a bad position. It was never easy out there batting and but credit to Will and Dimitri - they showed spirit and determination. We hoped to start the season with a win and now it's up to us to maintain this good start."
In the First Division, champions Sussex had to make do with a draw away to expected title rivals Surrey at The Oval.
Sussex were on course for victory when Surrey collapsed to 88 for seven with Mohammed Akram (four for 85) and Robin Martin-Jenkins (three for 47) in the wickets.
But Scott Newman's 86 helped steer Surrey to safety with former England Test bowler Martin Bicknell weighing in with a useful 37.