Brighton had leapfrogged the Magpies after beating Leeds on Friday night but Newcastle bounced back in style from two successive league defeats with a comfortable win.
Gayle put the hosts in control with two goals in seven first-half minutes and Yoan Gouffran added a third soon after the break before Gayle completed his treble to take his tally to 16 for the season.
The game of the day was at Molineux where Wolves and Fulham shared an eight-goal thriller.
Kortney Hause put Wolves ahead but Fulham took control with three goals in the space of 11 minutes from Stefan Johansen, Floyd Ayite and Tom Cairney.
Matt Doherty sparked the Wolves fightback in the 65th minute, Ivan Cavaleiro equalised and Dave Edwards looked to have won it in the 90th minute, only for Ayite to head a last-gasp leveller.
Reading kept the pressure on the top two with a 2-1 win at home to fellow promotion hopefuls Sheffield Wednesday.
Roy Beerens broke the deadlock in the 57th minute with a deflected shot and the Dutch winger added a second before Steven Fletcher grabbed an injury-time consolation for the visitors.
Huddersfield secured their first victory in six matches after beating Bristol City 2-1 at home to move up to fourth.
Elias Kachunga's early header was cancelled out by Tammy Abraham but the Terriers regained the lead when Nahki Wells punished City goalkeeper Frank Fielding's failure to deal with a backpass.
Norwich failed to build on their thrashing of Brentford last week as they slumped to a sixth defeat in seven matches with a 2-1 loss at Barnsley.
Tom Bradshaw and Conor Hourihane put the Tykes in control at the break and Nelson Oliveira's goal seven minutes into the second half was not enough for the visitors.
Cardiff earned a 1-1 draw at Ipswich despite the bizarre behaviour of Sol Bamba.
Aron Gunnarsson's opener for Cardiff was cancelled out by Luke Varney before Bamba was sent off for reacting angrily to a challenge by Jonathan Douglas, while he also clashed with the referee, the fourth official, his own physio and manager Neil Warnock.
Brentford ended a four-game losing streak with a 2-1 win at home to Burton thanks to Scott Hogan's double, either side of Jamie Ward's equaliser.
At the bottom, Rotherham claimed only their second win of the season thanks to Isaiah Brown's solitary strike at home to QPR but Wigan were denied a point by a superb 88th-minute strike by Jack Grealish which lifted Aston Villa into the top half.
Source : PA