The Blue Bulls fly-half kept his nerve before being mobbed by his team-mates after South Africa took an unassailable 2-0 series lead following their win in Durban last weekend.
It was the cruellest of blows for a wonderfully committed Lions side to take.
Stephen Jones had earlier kicked 20 points and full-back Rob Kearney scored a first-half try, but the world champion Springboks kept plugging away during an unforgettable contest of brutal intensity.
The Lions suffered blow after blow - props Gethin Jenkins and Adam Jones, plus centres Brian O'Driscoll and Jamie Roberts all went off injured - yet they refused to lie down until the last-kick drama.
It was a record seventh successive Test defeat on tour for the Lions, who now only have pride left to play for in Johannesburg next Saturday.
They have not won a Test series since toppling the Springboks 12 years ago, and questions will inevitably be asked about their future role in an increasingly demanding professional sport.
But they pushed South Africa to the wire - and beyond - before slumping to their knees as Steyn bisected the posts.
The Lions had heroes everywhere - no-one more so than 35-year-old lock Simon Shaw, whose magnificent Test debut gained its deserving reward when he was named man of the match.
South Africa kept themselves in the contest as Bryan Habana, his fellow wing JP Pietersen and substitute centre Jaque Fourie scored tries, the latter just six minutes from time following lengthy deliberation by Australian television official Stuart Dickinson.
Steyn added 10 points from the boot, while his namesake Francois slotted a long-range effort, and the Lions were thwarted.
It was a game that had everything, and is still not over for Springboks flanker Schalk Burger, who must surely be facing a disciplinary hearing tomorrow after he clearly eye-gouged Lions wing Luke Fitzgerald inside the first minute of the match.
Referee Christophe Berdos opted for a yellow card for Burger, who was winning his 50th cap, but television replays suggested it should have been red, with Burger now looking certain to be cited by the match commissioner.