Hearts, aiming to become the first side outside the Old Firm to win the title in 41 years, have led the league almost all season.
But their advantage over Rangers, which once stood at 13 points, is down to two after Danny Rohl’s men twice came from behind to win a thriller at Ibrox.
Chermiti was much-maligned during the early months of his time in Glasgow following an unproductive spell at Everton.
But five of the Portuguese under-21 international’s seven goals for the club, have now come against Hearts and Celtic.
The Jambos lost for the first time in six meetings against the two Glasgow giants this season despite twice taking the lead in the first half through Marc Leonard and Claudio Braga.
Michael Steinwender’s own goal briefly brought Rangers level and Chermiti made the most of a kind break of the ball to equalise for a second time before half-time.
Chermiti then powered in a header from Andreas Skov Olsen’s cross to put Rangers in front just before the hour.
He completed his first career hat-trick with a calm finish on the counter-attack in the 90th minute as the visitors chased an equaliser.
Celtic are three points off the top and have a game in hand over both their title rivals after a second-half revival at Rugby Park.
The Hoops, who have won 13 of the last 14 Scottish Premiership titles, were headed towards a damaging defeat when goals from Tyreece John-Jules and Joe Hugill gave Killie a deserved half-time lead.
Interim Celtic boss Martin O’Neill responded with a triple change and was rewarded with a second-half display which extended his unbeaten domestic run during two caretakers spells in charge this season.
One of the substitutes, Sebastian Tounekti, curled a strike into the top corner to get Celtic going.
The visitors quickly levelled when Benjamin Nygren profited from some slack Kilmarnock defending from a long throw.
But it took them until the 96th minute to find the winner when right-back Julian Araujo blasted in on his weaker left foot to spark wild scenes of celebration among the travelling support.
It is the third game in a row that O’Neill’s men have scored a vital goal deep into stoppage time.
“It’s not great for my health. It’s really draining, honestly,” said the 73-year-old.
“Obviously, it’s unbelievably satisfying to win, and to win in the manner in which we did at the end was terrific.” (AFP)
Edited by Cecil Wong
