Both sides entered the competition at this second qualifying round stage, and it was the side in the midst of their domestic campaign who were by far the sharper, taking the lead in the 12th minute when Lucas Lingman teed up Liam Moller.
Moller then turned provider 20 minutes later, setting up Pyry Mentu to put the hosts in control, before half-time provided only short respite for Coleraine, as Toivo Mero made it 3-0 just two minutes into the second half.
HJK introduced Teemu Pukki midway through the second period, and in the final 10 minutes, the striker rolled back the years, adding two goals in two minutes to all but put the tie out of the Bannsiders' reach ahead of the second leg on 30th July.
Ilves will have to win their second leg back in Tampere after falling to a narrow loss to Icelandic side Stjarnan. Both sides had come through the first qualifying round, but Ilves were unable to put in a repeat performance on the road after beating Differdange last time out.
After an even first half that lacked goalscoring opportunities, the home side dominated the second 45 minutes, not allowing Ilves an effort on goal before finally making the breakthrough six minutes from time through Gudmundur Nokkvason.
The Finnish side were unable to mount a response, but will have to in the second leg on 30th July if they are to keep their European campaign alive.