Alex McLeish won two league titles on the final day of the season during his time at Rangers and he is tipping his old club to do it again on Sunday.
Rangers will be champions if they beat Dundee United but can be caught by Celtic if they drop points.
"Rangers have the edge but have to go to Tannadice and win," said McLeish.
"United could be like world-beaters, but you have to think of what's at stake for Rangers - and that's why I think they will win it this weekend."
United need a point to be sure of fourth place and a Europa League spot, while Rangers have not won on their last five visits to Tannadice, drawing three and losing two.
Celtic, who are two points behind Rangers but with a superior goal difference, are at home to Hearts.
It's hard to call it but the odds might slightly be in favour of Celtic
Roy Aitken
"Dundee United have got something to play for, but Hearts have secured a place in Europe and can play relaxed football and make it difficult for Celtic," added Birmingham boss McLeish, who left Rangers in May 2006.
"Celtic have the experience of winning the last three titles and know what it takes, but Rangers have massive experience in terms of those who have played at the highest level."
McLeish's assistant at St Andrews, Roy Aitken - a former Celtic captain - takes another view on the forthcoming final-day drama.
"It's in Rangers' hands and it's like a cup final scenario, there's only one last bite at the cherry," said Aitken, who spent the first 14 years of his career at Celtic Park.
"Celtic must win and Rangers know a draw might not be enough.
"Both clubs have the mentality when they are expected to win their games each week, but it will need strong players. Each club demands success.
"Gordon Strachan is the first Celtic manager to win three consecutive titles since Jock Stein and four would be a a great achievement, whereas Rangers are desperate to stop the rot.
Celtic are title favourites - Aitken
"Rangers haven't won at Tannadice for a long time and that puts added pressure on them.
"It's in their own hands, which is always a good thing. If you get it right on the day then no-one can catch you and that's positive.
"But the (Rangers) record at Tannadice is dodgy, while Celtic can put pressure on them by getting a good early lead against Hearts.
"It's hard to call it, but the odds might slightly be in favour of Celtic."
McLeish, who led Rangers to the 2005 title when Celtic slipped to a dramatic late defeat at Motherwell and clinched the 2003 honours on goal difference thanks to a last-gasp penalty, knows the losing manager will get little credit despite the closeness of the championship race.
"In Walter Smith and Gordon Strachan, it's two legends in Scottish football locking horns," he said.
"Whoever wins will be great and whoever loses will get pelters from some quarters. That's the world we live in."
Aitken can also draw on experience of final-day drama success, since he was part of the Celtic team that chipped away at Hearts' lead in 1986, eventually clinching the Premier League trophy on goal difference after the Edinburgh side's defeat away to Dundee.
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