Scotland striker Nisbet grabbed his 17th goal of the campaign after just seven minutes before Boyle doubled the home side's lead with a penalty.
The visitors scored a spot kick of their own through Jay Emmanuel-Thomas with five minutes left – reward for a vastly-improved second-half display.
Hibs went into the game without Josh Doig, one of two changes to the team that beat Stranraer in the Scottish Cup on Sunday, after the highly-rated left-back sustained a shoulder injury at the weekend.
However, that did not upset the balance to the Leith outfit after Jack Ross' team stormed into a two-goal lead inside 26 minutes.
The opener arrived following a flowing move that carved open a static Lions rearguard. Paul McGinn played in Boyle and the winger, who could have shot himself, played a pass along the six-yard box for Nisbet to tap in.
Livingston, who were likely feeling the effects of Saturday's penalty shoot-out defeat to Aberdeen in the cup, had offered very little going the other way and the hosts doubled their advantage from the pot through Boyle.
He dusted himself down having won the spot-kick after going down under a challenge from Efe Ambrose before sending goalkeeper Max Stryjek the wrong way.
Livingston manager David Martindale had seen enough and brought on Jack McMillan for Jackson Longridge two minutes later.
Hibs continued to press and Livi goalkeeper Stryjek had to look lively to get down to Nisbet's low drive at his near post before watching Jackson Irvine head wide from the resulting corner.
Martindale then brought on Alan Forrest at the break as the Lions looked to get a foothold in the game.
Craig Sibbald did briefly threaten with a low deflected drive from 20 yards that forced Ofir Marciano into a save.
Another of Livingston's substitutes, Matej Poplatnik, almost made an immediate impact after coming on in the 67th minute when he directed Nicky Devlin's cross just wide at the far post.
The visitors were vastly improved as Hibs struggled to match their opponent's energy levels and Forrest hooked a shot wide from inside the area when he should have scored.
Livi did score from the penalty spot after striker Emmanuel-Thomas was felled by Kyle Magennis in the box but it was too little, too late.