Hearts flew out of the blocks, clearly buoyed by the fine performance last weekend, out-thinking and outplaying Omonia from the first whistle.
They pressed high through Shankland, Spittal and Kenneth Vargas and repeatedly won the ball back in Omonia territory.
It only took 16 minutes to find the opener. Spittal had a shot blocked inside the area, but it bounced nicely for Forrest, who controlled in the box and lashed into the top corner with his weaker left foot.
Frankie Kent nodded a corner wide when he should have scored and Shankland almost made it two, only to be denied by a brilliant diving save from Fabiano.
The captain, though, helped set up the second.
Receiving a throw in the box, he backheeled to Spittal, who curled in from close range - his third goal in three games.
The former Motherwell midfielder then went close to his second and Hearts' third, driving at goal and firing a shot inches past the post from just outside the box.
Shankland dragged another shot wide, before another was blocked off the line, and there was a feeling it just was not his night.
The second half was a quieter affair. Omonia did hit a post but the play was eventually pulled back for an offside, and Hearts suffered the same fate when Jorge Grant's tap-in was chalked off.