Ireland overcame playing 57 minutes a man short to shock the Springboks 26-20 on Saturday and clinch a landmark first victory in South Africa.
Flanker CJ Stander was red-carded for a dangerous tackle, but it did not stop the visitors winning a Test in the republic for the first time after seven defeats since 1961.
French referee Mathieu Raynal also yellow-carded Springboks lock Lood de Jager and Ireland centre Robbie Henshaw during the opening half of the first Test.
South Africa were a major disappointment under new coach Allister Coetzee and new captain Adriaan Strauss, looking lethargic for much of the game.
The teams meet again next Saturday in Johannesburg and in Port Elizabeth on June 25.
Only eight Springboks who started in the World Cup third-place play-off victory over Argentina last October began their first Test this season.
Those missing included retired centre Jean de Villiers and lock Victor Matfield and winger Bryan Habana, who is set to play in the Rio Olympics sevens.
And the preference of Coetzee for local players meant no call-ups for France-based hooker Bismarck du Plessis and prop Jannie, his elder brother.
Lambie was right and wide with an early long-range penalty attempt before Ireland took the lead on 11 minutes in cool, windless conditions.
A clever kick behind the defence close to the try-line by centre Luke Marshall allowed full-back Jared Payne to race in and dot down.
De Jager was yellow-carded for foul play during the build-up to the score.
Fly-half Paddy Jackson, deputising for injured star Johnny Sexton, converted and slotted a penalty to give the Irish a 10-3 lead.
Ireland were reduced to 14 men after 23 minutes when a late tackle by South Africa-born Stander floored Lambie and he was sent off.
Elton Jantjies, who replaced the concussed Lambie, kicked a simple penalty, then his brilliant inside pass sent left wing Lwazi Mvovo over to score.
Henshaw made a late, high tackle on Jantjies during the build-up to the score and was sin-binned.
Despite being two men short, the visitors equalised three minutes before half-time with a Jackson drop-goal making it 13-13 at half-time.
Three minutes into the second half, Ireland regained the lead when scrum-half Conor Murray dotted down after a good Payne off-lead. Jackson converted.
As the game entered the final quarter, a hushed Newlands stadium signified the frustration of Springbok fans as the team struggled to make a numerical advantage pay.
A Jackson penalty stretched the advantage to 10 points before his pass was intercepted by lock Pieter-Steph du Toit, who raced over and Jantjies converted.
But another Jackson penalty closed the scoring and a late Springbok surge to try and grab an undeserved win ended with winger JP Pietersen bundled into touch.