Instead, despite being the outright favourite, he was beaten 6-3, 6-7 (7/4), 7-6 (7/3), 6-4 by a 17 year-old German upstart who became the youngest Wimbledon champion and also the first to win the prized title as an unseeded player.
Boris Becker went on to annex three Wimbledon titles while reaching the final seven times.
Curren was left licking his wounds, with the consolation that he remains to this day alongside Brian Norton, a finalist way back in 1921, the only South Africans to have reached the blue riband men's singles final at Wimbledon.
In what Curren, now 57, describes as "the most memorable, but also most disappointing day of my tennis career," the languid, but deceptively devastating big-server from Durban believes the seeds of his defeat against Becker were planted in his very first service game in the first set of the final.
Curren had been the sensation of Wimbledon up to that point, having beaten world number one John McEnroe, Jimmy Connors, who was not that far behind in the rankings, and Stefan Edberg, a future Wimbledon champion, without dropping his service once on Wimbledon's lightning-fast grass courts.
"My service had been in the zone and had been virtually unplayable," says Curren, "with the bookmakers consequently making me an outright favourite for the final.
"But as fate would have it, I immediately dropped my first service game of the tournament in the final and Boris went on to win the first set.
"It jolted me and probably gave him the confidence and belief that he could win the match - although, admittedly, he played throughout with lethal poise, especially for someone so young."
Curren recalls that he fought back in what turned out to be an uncompromising battle of big servers, won the second set via a tiebreaker and broke service first in the third set to briefly go ahead for the only time in the game.
"But nothing seemed to deter Boris," says Curren. "He broke back almost immediately in the third set, won it in the tiebreaker and then edged me out with a single break in the fourth and final set.
"In all, I dropped service three times in the game, Boris only once."
Curren says that when he met McEnroe some time after the game, the brash New Yorker proclaimed "you blew it, hey!"
"But" added Curren, "some time later after McEnroe had barely beaten Becker in a ding-dong struggle, John came back to me and apologised.
The kid is a helluva player, he said."
Today, Becker at 47 is back in the limelight as joint coach of world number one Novak Djokovic after a stormy, at times controversial career that earned him seven grand slam titles.
While Curren had a brief spell as captain of the South African Davis Cup team after retiring as a player, he says he has no designs about returning to tennis in a similar role to that which Becker now occupies.
"Perhaps it might have been attractive when I first gave up playing," he added, "but now I've got other challenges in life as a keen golfer, organising golf tournaments and other business interests."
But he remains one of South Africa's most decorated tennis players, having reached two grand slam singles finals - losing an Australian Open final against Mats Wilander in addition to that against Becker - while annexing one grand slam men's doubles title and three mixed doubles titles.
He also reached a world ranking of fifth, bettered among South Africans only by Eric Sturgess and Cliff Drysdale who both made it to four in the world.
Curren won five ATP singles titles and his serve-and-volley game made him a superb doubles player with 26 ATP men's doubles titles from 53 finals.
But despite all the glory days, that defeat against "Boom Boom" Becker still rankles more than somewhat.