The only way a unicorn could possibly hurt the dragon would be if it lowered its horn and charged straight at the dragon. This tactic could work, but has several flaws. Here is one, the dragon is probably used to pesky humans on horseback charging it with spears/lances, so the unicorn's tactic isn't a huge surprise for it.
unicorns r extremely fast so fast that its said the only way to catch them is to lure them with a virgin however if the virgin is just pretending to be a virgin then it would tear her to pieces. so it would be next to impossible for a dragon to burn it or grab it and if the dragon had toxic breath like some do then the healing ability of its horn would make it just bad breath
and lets not forget there hooves they could use those with there deadly speed mentioned prior to crush a dragons skull also a unicorn was originally depicted to have two horns so that would give them a greater chance of killing a dragon when raming them.