Requiring 245 runs for victory, the hosts were in control on
127-1, with Mark Wagh and Bilal Shafayat at the crease – but their departures for 70 and 49 respectively sparked a slump.
Charl Willoughby (three) and Alfonso Thomas (two) led the wicket takers and on 246-8 things were getting decidedly edgy. However, Amla settled the contest with a boundary which took his contribution to an unbeaten 64 from 73 balls – to inflict a second defeat of the season on Somerset.
Another team recording their second win in as many games at the start of the season were Lancashire, who defeated Essex by eight wickets at Chelmsford.
The match finished with more than four sessions to spare as Essex were bowled out for 173 in their second innings, leaving their opponents requiring just 38 to win.
Sajid Mahmood and James Anderson each picked up three wickets but it was captain Glen Chapple who claimed the most important scalp of the day in the eight-wicket success, England batsman Alastair Cook (50).
Durham face the prospect of opening their title defence with back-to-back home draws, although they did give themselves an outside hope of victory with three evening-session wickets against Hampshire.
The Durham bowlers toiled admirably to leave the visitors 174-5 and with a lead of 135 runs with a day to play – after an impressive display of swing bowling from Hampshire's Kabir Ali restricted the hosts to a first-innings lead of 39.
In Division Two, Greg Smith followed a career-best batting performance with four wickets as Glamorgan folded feebly to put Derbyshire in sight of victory.
Smith scored an unbeaten 165 from 329 balls and shared a last-wicket stand of 78 with Welshman Steffan Jones that earned Derbyshire a first-innings lead of 91 and took the game away from the visitors.
At Derby, only Gareth Rees offered any resistance as Glamorgan collapsed to 211 second time around, leaving Derbyshire a target of 121.
By the close the hosts were 26 for one, only 95 runs away from a second win of the season.
Sussex made it three successive wins by completing a 207-run victory over Gloucestershire inside three days at Bristol.
Corey Collymore and James Anyon each claimed three wickets for Sussex.