Motherwell were on the road for the third time in seven days as they travelled down the M8 to the capital to take on Hibernian in the cinch Premiership at Easter Road.
In a frantic first half, neither team could stamp their authority on the game.
At the start of the second period, Motherwell shouts for a penalty were waved away by Grant Irvine after Connor Shields went down in the area.
It would be Shields who would be involved in the biggest turning point in the match, after failing to clear the ball, Ryan Porteous raced through on goal but Shields pulled the defender to the ground and was shown a red card.
Porteous would get on the end of Boyle’s deflected cross to net the opener and subsequently, the winner.
With ten men on the park, Motherwell continued to create half chances but couldn’t find the equaliser and went back to North Lanarkshire empty handed despite a hearty showing from Steven Hammell’s men.