The South African struck 75 as the hosts posted a first-innings total of 290 on an overcast day that suited the bowlers.
James Vince also notched a classy 75 and Hashim Amla made 36 on his Hampshire bow.
In reply, Worcestershire were 40/2 at stumps.
With the visitors taking the option to field first, Hampshire lost Lewis McManus for just two in the third over.
But Vince - desperate for early-season runs to impress the England selectors - raced to his half century in just 49 balls as he put on a 106-run partnership with Jimmy Adams (33).
The captain looked every inch a Test batsman as he looks to to retain his berth as the Three Lions' number three for next's month's series against Pakistan, following a tough winter in Australia and New Zealand.
Vince was cruising before he was bowled by Steve Magoffin 25 runs shy of his ton.
Hampshire were well poised after posting a score of 131/3 at lunch but lost debutant Sam Northeast (17), Amla, Rilee Rossouw (naught), Liam Dawson (24) and Kyle Abbott (naught) in the afternoon session.
But Berg's high-risk, high-reward stroke play paid dividends and he moved the hosts to a decent first-innings total in the conditions.
The South African struck 75 and shared a 38-run last-wicket stand with Fidel Edwards (one) before the former West Indies bowler was dismissed by Leach and Hampshire were all out for 290 from 74.5 overs.
Worcestershire were forced to bat for 18 overs under the Ageas Bowl floodlights in their first innings.
And Hampshire made their breakthrough in the second over when Edwards' delivery found Brett D'Oliveira's leading edge, with Vince snaffling the catch.
Abbott almost had his revenge on Mitchell but the opener's edge didn't quite carry to Amla at first slip.
The former Proteas pace bowler also had two decent lbw appeals on Tom Fell turned down.
Fell soon started to open up his arms and hit Brad Wheal for successive fours in the 14th over.
However, the visitors' number three didn't have much more of an impact and was clean bowled by Abbott during his second spell for 16.
Worcestershire didn't lose any more wickets, though, with Mitchell (15 not out) and tailender Josh Tongue (four not out) set to resume play with the visitors on 40/2 tomorrow morning.