The League One champions face Raith Rovers at Easter Road on Sunday, aiming to add the silverware to their title and take another step towards what would be a remarkable treble this term.
Dundee United head to Ibrox for an eagerly anticipated semi-final clash just six days later and Andrews, who won the Premier League title and Scottish League Cup with Alex McLeish's side in 2005, knows the power of momentum in the closing stages of the campaign.
"If Rangers can win on Sunday it will give them a taste of cup success ahead of their semi-final with Dundee United the following weekend," he told SportTimes. "It would give them a big lift and they can then look forward to the Scottish Cup.
"Ally is under a lot of pressure and a lot of scrutiny but he has done well this season.
"He has led the team to the title already and if they can do well in the cups now it would make it a great season.
"They have done what they had to do this season, they have won League One handsomely.
"Now it is about adding to that by winning both cups if they can."
Andrews has seen Rangers at close hand as they have eased to the third tier title but it was his Forfar side who caused the upset of the campaign for the Light Blues by knocking them out of the League Cup in August.
Despite closing in on an unbeaten League One campaign, the Gers have come in for criticism for some of their performances as they have overcome their part-time rivals.
But Ibrox cult hero Andrews reckons the champions haven't got the credit they have deserved as they look to end the season in style with more silverware.
He said: "Rangers have handled League One really well this season. They have some good players that have played in the SPL and they have an experienced team mixed with some good young prospects that are coming through.
"Rangers will be favourites for the game but I am sure Raith will have something to say about that and be raring to go at the weekend.
"They are coming up against part-time teams but if you talk to the Rangers players they will tell you that each game they have played has been really tough for them and really difficult.
"They are full time and they have an advantage but it is not easy to do what Rangers have done this season.
"You can't take away the fact that Rangers have been by far the best team in the league this season and deserve to be champions."