IMO... IF they had to make the Cap win (well, they did have to), it should not have been a win through melee combat. At best, Cap should have somehow figured out a one and only weakness of the Chief. What that might be? No idea :P But maybe along the lines of the Chief giving up his life to save Cortana? (presuming Cap somehow managed to capture Cortana with capability to terminate, heh)

Really, from capabilities alone, MC shouldn't be beaten by Cap. But every hero has a weakness (typically some limitation of morality or ethics by which the 'bad guy' can entrap them). Cap would have had to find that weakness in order to beat him.
Fighting alone? uh uh.