Michele Fornasier and Ryan Tunnicliffe were both sent off in the second half in a hotly-contested encounter yet Michael Keane still found the net and ensured a nervous finale for the Brazilians.
Coritiba went ahead early on when Alex Santos converted a cross by Joao Amaral and the Reds' task was made more difficult when Fornasier received a second yellow card on 64 minutes. The South Americans took full advantage with Jose Vivian smashing past Sam Johnstone to double their lead.
Tunnicliffe, who had picked up a couple of bookings earlier in the tournament, was shown a straight red card for dissent and, with 17 minutes remaining, United's bid for success looked to be imploding. But Michael Keane showed what a threat he is at set-pieces by nodding home a Luke Giverin corner to reduce the deficit.
Johnstone kept his team in the match by denying William Henrique and there were late chances at the other end, with Larnell Cole going closest, but Warren Joyce's side had to settle for runners-up.