The South Africa international was trapped lbw by Josh Tongue, with the hosts losing five wickets in the second session and finished 237/8 at tea on the opening day's play.
Hampshire began on 131/3 after lunch, courtesy of a swashbuckling 75 from captain James Vince.However, the Ageas Bowl outfit lost debutant Sam Northeast for 17 when he was bowled by visiting skipper Joe Leach.
Rilee Rossouw was also sent back to the pavilion by Leach for a 10th-ball duck.
Amla - who surprisingly batted in the number-five berth as opposed to opening like many expected - was patient and got himself into a decent rhythm.
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The right-handed batsman notched 36 - including four boundaries - from 72 balls before being trapped lbw by Tongue's final ball of the 50th over.
Liam Dawson and Gareth Berg took up the mantle of steering Hampshire to a competitive first-innings total.
In overcast conditions which suited Worcestershire's bowling attack, the pair kept the scoreboard ticking along.
They shared a partnership of 40 before Dawson was bowled by Daryl Mitchell in the Worcestershire man's first over for 24.
And the right-arm medium pace bowler dismissed Kyle Abbott lbw for a golden duck the following ball.
Berg (32 not out) will be joined by Brad Wheal at the crease for the final session of the day.