Hampshire 222 (Leach 5-63) and 245 for 6 (Smith 64, Wheater 52, Leach 4-89) drew with Worcestershire 403 for 5 (Mitchell 142, Cox 69*)
Leach returned figures of 4 for 89 after collected a five wicket haul in the first innings - to end with match figures of 9 for 152. But heroic rearguard action from Smith and Wheater meant that both captains shock hands on a draw at 5.40pm with nine scheduled overs to play.
Hampshire started their day of blocking in the worst possible way when they lost opener Liam Dawson to the 18th ball of the day as Leach produced a snorting delivery to create an edge for wicketkeeper Ben Cox.
Michael Carberry lasted 18 balls before he was caught at short leg off Jack Shantry for a disappointing six - completing a forgettable game for the former England Test batsman, after he had scored 14 in the first innings.
James Vince used up 50 deliveries but departed five minutes before lunch to debutant Barnard for 12.
Hampshire captain Jimmy Adams had lead from the front in the morning session to reach a patient 47 but Leach had him leg before to the final ball of the morning - five balls after Vince had got out.
Wheater scored a second first-class fifty of the season but his wicket just before tea kept Worcestershire well on top at the Ageas Bowl.
Wheater - who was off the field earlier in the match having an x-ray on his finger - made his fifty in 95 deliveries. He hadn't past 14 in the Championship since making 74 at Warwickshire in April and when moving past 44 reached his 4000 career first-class run.
But Leach picked up his eighth wicket of the match by bowling a leaving Wheater, to end a frustrating spell for the visitors, as the wicketkeeper and Smith put on 68 for the fifth wicket.
And Sean Ervine was Leach's ninth victim as the Zimbabwean tamely chipped up for a simple catch for Tom Fell at short extra cover. Like Wheater, Smith also had time off the field on the second day, but looked healthy as he batted the whole afternoon and evening sessions for a sturdy unbeaten 31.
The sparsely populated temporarily stands came to life when Gareth Berg pushed Hampshire into a second innings lead, mean Worcestershire would have to bat again to win.
The second new ball was the last chance of hope for a Worcestershire victory - and Charlie Morris managed to find some extra bounce with the very first delivery with the new cherry, to catch the shoulder of Smith's bat but it dropped agonisingly short of second slip Mitchell. Smith who ended on an unbeaten 64 - who was given a county cap on the opening morning -continued in his trademarked style of watchfully waiting for the bad delivery to move to his fifty from 133 balls - before both sides agreed to a draw.