But, having played well to take Kim to a deciding set, he buckled under the pressure.
Elder reset his bow with just a few seconds left on the clock before landing a six and going down 6-4.
Kim, a bronze winner in the team event, regrouped after his near miss to see off Tarundeep Rai and reach the last 16.
Rai had earlier held his nerve in a 6-5 win over Juan Carlos Stevens, locating the nine ring in a one-arrow shootout.
Michele Frangilli could not recreate his Team event heroics as he was knocked out in the first round.
Frangilli ensured gold for Italy when he dramatically struck 10 with the last arrow of Saturday's final but his touch deserted him as Ukraine's world number three Dmytro Hrachov claimed a 7-3 victory.
Having already secured a gold, the veteran was not too downcast about his exit and is looking forward to getting to know his fellow Olympians.
'I will not go sightseeing now. I know London by heart,' he said.
'I will be here for the other Italians and then I will stay at the Olympic Village. I enjoy spending time there.'
Hrachov himself became a big-name scalp when he lost his last-32 encounter with Japanese fifth-seed Takahuru Furukawa.
Furukawa almost lost his first elimination match against Lee Kar Wai Calvin when the 60th seed took a 4-0 lead but hit back to win the next three sets.
He then saw off Hrachov 6-4 and will meet Norway's Baard Nesteng in Friday's round of 16.
In the women's event, world champion Denisse van Lamoen was dumped out in the first round.
Van Lamoen, who was Chile's flagbearer at the Opening Ceremony, was paired with the player she defeated for world gold in Turin last year – Georgia's Kristine Esebua – and was defeated in straight sets.
Both players were well short of their best in the ranking round, hence lowly seedings of 31 and 34 respectively, but Esebua found her feet to see off Van Lamoen 6-0.
Esebua could not pull off another big win, though, and was defeated by second seed Lee Sung-jin in the last 32.
Lee missed the gold rings only once in nine arrows on her way to a dominant 6-0 victory over Samoa's Maureen Tuimalealiifano and added another four 10s as she racked up a four-set success against Esebua.
Japan's Team bronze on Sunday was their first-ever women's Archery medal and their number one player, Ren Hayakawa, remains in the hunt for a second.
She coped admirably with an unhelpful rain shower to take a 6-4 win over Swede Christine Bjerendal in her opening clash before facing Russia's world number 10 Inna Stepanova.