"I must say there were a few nerves in the beginning," Meyer said. "Defence on both sides was unbelievable. I'm just happy we got through the first one."
England led 3-0 and 6-3 early on in Durban through first-five Owen Farrell's boot, but South Africa's powerful ball-carriers eventually wore down a brave defence to hand Stuart Lancaster just his second defeat in six tests in charge.
England wing Ben Foden scored in the final act with the result already settled, as South Africa's dominance for most of the second 40 proved decisive in the first of a three-test series.
"The set-piece was a good area for us," England forwards coach Graham Rowntree said, "but certainly going into the last quarter, they brought some fresh cattle, some fresh beasts, on to the field and there are some areas to work on as always against these big teams."
Steyn's 48th-minute try pushed South Africa ahead after it struggled to break down England's gutsy rearguard.
De Villiers' score gave the Boks a 16-6 advantage, which was ultimately too much for England to claw back despite Farrell's kicking and Foden's late diving try in the right corner after the final hooter.
South Africa overcame a rusty start after just a week of preparation under Meyer, and needed to dig deep against an England team which resisted until the end despite its inexperience.
The teams meet again at Johannesburg and then Port Elizabeth to decide the first three-test series in South Africa since 1996.
Relieved Wallabies coach Robbie Deans has predicted a brilliant three-match series which could go down to the wire after an enthralling 27-19 triumph over Wales on Saturday .
Australia bounced back emphatically from their disastrous 9-6 upset loss to Scotland by clicking into gear to unlock the strong Welsh defence at Suncorp Stadium.
But despite their three-tries-to-one triumph, to continue the tourists' 43-year drought Downunder, the Wallabies only escaped after withstanding a spirited second-half comeback by the tourists.
Down 20-6 with 30 minutes to play, the Red Dragons fired and Australia's defence tired as they hit back to close the gap to one point with 17 minutes left.
Wales could have hit the lead if not for five-eighth Rhys Priestland uncharacteristically bombing a try by dropping a high pass with a three-man overlap outside him, while they also fumbled at other crucial times.
"We just didn't take those opportunities in the second half," Welsh coach Rob Howley lamented.
"We probably left two or three tries out on the park, to be honest."
In the end, man of the match Will Genia sent centre Pat McCabe, running a brilliant angle, over for the clincher.
Deans praised under-pressure playmaker Berrick Barnes who produced a fine all-round game and showed good vision to help orchestrate his first win in eight matches.
But it was Genia who was the stand-out, highlighted by a solo 35m try after halftime where he split two tight-forwards and then stepped around fullback James Hook.
Argentina reeled off three straight tries when the Italians closed within a point in their one-off test yesterday.
After halfback Edoardo Gori's try in the 51st minute cut the Pumas' lead to 16-15, prop Rodrigo Roncero responded three minutes later, No 8 Leonardo Senatore crossed for another converted try to make it 30-15 and captain Felipe Contepomi added another with eight minutes to go. Italy crossed late but couldn't prevent a third straight defeat to the Pumas.
South Africa 22
England 17
Australia 27
Wales 19
Argentina 37
Italy 22
- Agencies
