Rangers are now 7/2 to win the Scottish Premiership after Celtic dropped points again on Sunday.
Steven Gerrard's side, 7/1 on the opening day, have seen their odds shorten with online bookmaker Sky Bet after a good start to the season.
They sit second in the table, five adrift of early leaders Hearts (still 25/1 to finish top), while Brendan Rodgers' Celtic, who remain odds-on favourites, are sixth.
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See a summary of Sunday's action, below...
Brendan Rodgers admits he is facing the biggest test of his Celtic tenure after their 2-1 defeat at Kilmarnock confirmed the Hoops' worst start to a Ladbrokes Premiership season in 20 years.
Defender Stuart Findlay's dramatic injury-time header from a Chris Burke corner gave Killie a stunning victory, after Burke's drive had cancelled out Leigh Griffiths' first-half opener.
The Northern Irishman has enjoyed nothing but domestic success since arriving at the Parkhead club in 2016 and his side finished last season as unprecedented double treble winners.
However, after six games the champions have only 10 points and are six points behind leaders Hearts, their poorest start since the 1998-99 campaign under Jozef Venglos.
Asked if faced the biggest challenge of his time as Celtic boss, Rodgers, who will have defender Filip Benkovic's Achilles problem assessed after he pulled up in the warm-up, said: "It is. It's a challenge.
"We have to accept that. There's no doubt we need to be better. When you're at the biggest clubs and you don't win the heat comes on to you.
"That's when you show you're a Celtic player, manager, member of staff.
"You come together. When you lose games the spotlight will always be on you.
"You have to work hard, do the basics right. The basics cost us this time.
"It hasn't been great, but we have to accept that. We're the only ones who can make it better and get more consistent results."
Celtic have lost to Hearts and Kilmarnock and have drawn with St Mirren in the league.
Rodgers believes opponents are getting better, while also having a "new-found respect" for his side.
The former Liverpool and Swansea City boss said: "The teams are playing deep. At St Mirren we saw it, even when we had 10 men. You saw Rangers come and sit deep, Kilmarnock did that too.
"It's up to us, we have to find the answers to that. That's the job.
"We have to analyse the game and build the mentality again to win your next game.
"I'd have been disappointed to draw, but to lose is bitterly disappointing. It was a scrappy sort of game, but I still feel we had the better moments and more control."
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Rangers moved up to second in the standings after thrashing St Johnstone 5-1 at Ibrox.
James Tavernier opened the scoring in the ninth minute with his free-kick on the edge of the box before Alfredo Morelos cut in from the right to smash past Zander Clark after the half hour.
Scott Arfield rifled home on the rebound to put Gers well on the way to three points in the 52nd minute, while substitute Kyle Lafferty scored on the counter with a quarter of an hour remaining.
Blair Alston tucked home a late penalty after being tripped by Connor Goldson, but it was scant consolation on a painful day for Saints, who remain in eighth place.
Their misery was compounded when Daniel Candeias struck in the 79th minute, taking his time to finish off after being teed up by Arfield.