Christian Doidge, Kevin Nisbet and Martin Boyle struck at Stair Park to set up an Easter Road clash with Motherwell next weekend.
The trio have now netted their team's last 11 goals between them.
It took Hibs 37 minutes before Doidge opened the scoring, but the first half was one-way traffic and Nisbet's deflected strike gave Jack Ross's side a cushion just when it looked like they might need one.
Boyle then struck a double including one from the spot to take his personal tally to nine in 11 matches.
Hibs were on the attack from the off. Josh Doig drove a ball across the face of goal in the opening moments and Boyle was causing havoc on the right flank.
Boyle twice set up Nisbet, who missed the target each time, and forced a save himself from long range.
The winger then set up Paul McGinn, whose shot was pushed over by Greg Fleming.
Hibs made the breakthrough from the resulting corner. Doidge had twice been denied by blocks earlier in the game but found a way through this time as he turned and hooked a bouncing ball into the corner of the net.
The home side had a decent spell, forcing some set-pieces and then suffering some misfortune when Tam Orr's goal-bound effort struck team-mate Darryl Duffy after Connor McManus had cut the ball back.
The visitors doubled their lead in the 64th minute when Nisbet's 25-yard free-kick hit a Stranraer head in the wall and wrongfooted Fleming.
Boyle struck seven minutes later with an emphatic finish on the rebound after Nisbet had headed against the post.
Boyle and Nisbet came close before Doidge headed against the bar and the winger thrashed home the fourth in the 84th minute after Porteous had been tripped.
Matt Macey made a couple of decent saves to deny James Hilton and Matty Yates as Stranraer pushed for a consolation goal.