Monaghan lost 3-12 to 0-14 at home to Galway, ending their hopes of staying in the league, while David Clifford led Kerry to a 0-18 to 1-11 win over Tyrone in Division One.
Clifford scored 0-8 and Kerry almost secured their place in Division One, while Tyrone were by no means safe as they suffered their third defeat in the league.
Ciaran Daly's Tyrone goal at Killarney was too little too late.
Galway's goals came from Cathal Sweeney, Rory Cunningham and John Maher late in the first half against the Clones.
Major took Galway from 3-4 to 0-7 at the interval, and even the introduction of Conor McManus, making his first appearance of the season, failed to spark Farney's rally as the Tribesmen continued to dominate.
Tyrone gets lost in the scuffle.
At Fitzgerald Stadium, Tyrone led several times in the first quarter but lost their way midway through the first half when a scuffle broke out.
Kelly scored six points in a row on either side of the break, taking the game completely away from Tyrone.
The Redhands were already short-strength, but they lost Peter Hart and Con Kilpatrick to injuries during the game, giving their young, inexperienced players a reality check against one of the best teams in the country. Ta.
Tyrone converted just six of their 15 scoring chances in the first half, with Niall Morgan crediting Sean O'Shea for some strong body saves.
Paudie Clifford, like his brother, played with great presence, and with the supporting cast playing their part, he finished the game with an 0-3 record.
Diarmuid O'Connor got through a lot of work and showed some well-linked play in the middle third.
Darragh Canavan struggled up front, picking up three points from Tyrone's play, but with little support.
He finished a long 19 minutes without scoring for Tyrone either side of half-time, but Kerry were relentless and enjoyed the space and room they were given to run into.
With plenty of space and time, Tyrone's forwards couldn't afford to miss out on what would be a long and difficult afternoon. Tyrone are targeting a must-win home game against relegation-threatened Monaghan on Saturday week.
Monaghan remain bottom of the table
Monaghan remain at the bottom of Division One after losing by seven points to compatriots Galway in Clones.
Padraig Joyce's team's three goals in the first half gave the Westerners a foothold in a game they never wanted to give up.
The absence of goalkeeper Rory Beggan was felt once again as Monaghan's defense struggled to deal with high balls.
With two games remaining, Vinnie Coley's side remain in the standings with just one win from five games.
In a closely contested first quarter, Jack McCarron's 25th-minute free shot gave Monaghan a deserved lead at 0-4 to 0-3, but Andrew Woods' black card four minutes later gave the visitors a deserved lead. It was misused.
Quick-break goals from Sweeney and Cunningham in the 29th and 31st minutes gave Galway a six-point lead.
Initially, Monaghan responded quickly and aggressively, taking three unanswered points from McCarron, Michael Bannigan and Michael Hamill.
But just before the half-time whistle, another high ball into Monaghan Square caused panic and Galway midfielder Maher pounced on it to score the third goal.
This was a terrible punch from which Monaghan never recovered, and the Galway defense was able to repel Monaghan's attacking advances, including McManus.
Galway moved up to fifth place with five points, with Cillian O'Claoin and Cunningham keeping the scoreboard moving. Monaghan now have to rebuild their team ahead of a major relegation battle with neighbors Tyrone in two weeks' time.