Substitute Gow found the net with minutes left although the result was already beyond doubt by that stage.
Colin Nish notched a first-half brace while Derek Riordan and Abdessalam Benjelloun also got on the scoresheet.
Montrose midfielder Chris Hegarty had his moment of glory with a 25-yard drive that edged past Graeme Smith.
The Third Division basement side wasted a great chance to take a shock lead in the fourth minute when Ian Murray was caught as he tried to guide the ball out of play at the byline.
Stevie Nicholas stole the ball and pulled the ball back for Hugh Davidson but he mis-kicked from 12 yards.
That moved spurred the hosts into action as they took the lead just 60 seconds later.
Derek Riordan's low drive from 18 yards was only blocked by goalkeeper Andy McNeil and Nish was on hand to force the ball over the line.
John Hughes' side looked to add a second just moments later but Riordan's stinging effort from just outside the area was palmed over the bar by McNeil.
Things went from bad to worse for Montrose when John Maitland was forced off injured in the 10th minute, with Marek Tomana his replacement.
Referee Alan Muir waved away Hibs shouts for a penalty when Anthony Stokes fell to the ground under a challenge from McNeil, awarding a goal kick instead.
It was no surprise when Hibs doubled their advantage in the 26th minute through Nish, who headed in John Rankin's cross at the back post.
With Montrose short of ideas in the final third, midfielder Chris Hegarty unleashed a venomous free-kick from 25 yards that was spilled by Graeme Smith but his team-mates were on hand to stifle the danger.
Hibs' first chance of the second half came after 55 minutes when Miller rolled in Riordan but his cross-cum-shot from an angle drifted wide.
Riordan then tried to pick out team-mate Stokes with a deft pass into the area but McNeil came rushing from his line to smother the ball.
Montrose were refusing to throw in the towel and a piercing Milligan run left Nicholas with a sight of goal but his effort was blocked by Chris Hogg.
McNeil came to his side's rescue again with a superb double save in the 68th minute.
He got a strong hand to substitute Merouane Zemmama's left-footed strike and then scrambled across his goal to deny Nish a hat-trick, pushing the striker's shot wide.
However, the keeper was left clutching at air when Riordan scored his side's third in the 69th minute with an unstoppable 30-yard drive that flew into the top corner.
Hegarty notched his side a consolation goal in the 75th minute as he powered a low 25-yard effort past Smith.
Hegarty, son of Dundee United legend Paul, picked up a booking after celebrating with the Montrose supporters behind the goal.
Hibs restored their three-goal cushion three minutes later, however, when Zemmama crossed for fellow substitute Abdessalam Benjelloun to head in from close range.
Keeper McNeil was doing his bit to keep the score respectable, getting down well to block Riordan's low shot.
However, substitute Gow capped his maiden appearance with a superb solo effort as he cut in from the left flank and showed great skill inside the box before slotting the ball into the corner of the net in the 88th minute.