Livingston narrowed the gap via a Lyndon Dykes penalty but Nisbet claimed the match ball by rolling in a spot kick of his own two minutes from time.
The first chance of the game went the way of the home side. Dykes did well to fizz a ball across the six-yard box for Robinson who could not steer his shot inside the near post.
Doidge then could have marked his return to the side with a goal but glanced his header from Joe Newell's cross wide of target.
His strike partner, though, would fare better after 15 minutes. Horgan fired in a cross from the left that the Livingston defence fared to clear, giving Nisbet a chance for a tap-in for his first Hibs goal following his summer move from Dunfermline.
Hibs continued to look the more threatening but it was Livingston who had the next chance, although Robinson's deflected free kick lacked the pace to trouble Ofir Marciano.
Instead it was the visitors who struck again after 38 minutes with the same pair combining to good effect. Horgan's delivery this time was floated to the back post where Nisbet rose highest to power in a header.
It was 3-0 before half-time. A Newell corner was not cleared and Hibs scrambled the ball to Doidge who tapped in at the back post for his first goal of the season.
Livingston reacted by making two changes at half-time and gave themselves a lifelong on the hour mark when they got a goal back from the spot.
Nisbet completed his hat-trick from the spot late on after Marvin Bartley had fouled Newell in the box.