Set 485 to win, Kent were in dire straits at 380 for eight with more than two hours left on the final day of four.
However, tailenders Min Patel and Simon Cook kept Hampshire at bay, Kent passing 400, before Cook was bowled by leg-spin legend Warne for 37.
But former England left-arm spinner Patel (41 not out) found another ally in last man Amjad Khan, who survived 10 balls against Warne and England pace prospect Chris Tremlett, as Kent finished on 447 for nine.
The draw, in a match that had earlier featured Warne's maiden first-class hundred and a century from Hampshire's rising England star Kevin Pietersen, left the visitors just a point behind Nottinghamshire and reigning champions Warwickshire at the top of the table.
In the day's other top-flight match Surrey paceman Mohammad Akram took four for 63 as Glamorgan were beaten by 276 runs at The Oval.
After a stand of 171 between Glamorgan's David Hemp and Mike Powell, who both fell in the 90s, the Welsh county lost their last seven wickets for 28 runs as they collapsed to 248 all out.
In the Second Division, Worcestershire needed just 65 minutes' play to complete a nine-wicket thrashing of basement county Derbyshire.
Graeme Hick, now almost as much a part of the scenery at New Road as the cathedral overlooking the ground, finished on 62 not out.
Elsewhere another former England batsman, Anthony McGrath, struck an unbeaten 165 as Yorkshire beat Leicestershire by six wickets at Grace Road.
Yorkshire's score of 406 for four was the highest fourth innings total to win a match in the county's history.
Ahead of Sunday's announcement of the England squad to play Bangladesh in this month's first Test at Lord's, Yorkshire's huge total also featured 53 from England captain Michael Vaughan.
Australia all-rounder Ian Harvey chipped in with 47 before he was bowled by Phil DeFreitas - now the only member of the 1986-87 England squad, the last to win the Ashes, still active in first-class cricket.
Elsewhere Essex, with former Zimbabwe captain Andy Flower making an unbeaten 142, resisted gamely to force a draw against Northamptonshire.
Essex were made to follow-on after being bowled out for 178 in reply to their hosts 552 for seven declared.
But they fared much better in their second innings with promising opener Alistair Cook, 131 not out overnight, falling just five runs short of a double century in a total of 495 for six declared.