While Scott Johnson's men were starved of possession in their last outing against Ireland at Murrayfield, a solid defensive performance provided the sturdy platform for a smash-and-grab 12-8 victory.
But Hastings believes that the rejuvenated Welsh will play a far more open game that will provide the opportunity for the Scots backs to cut loose.
The 64-times capped Scotland great also believes that big performances from Stuart Hogg, Sean Maitland and Tim Visser could go a long way to booking their place on the British Lions of Australia this summer.
Hastings said: "While the Ireland game was all about defence I think this game could be all about attack.
"The Welsh like to go through the phases and play with ball very much in hand and I think that will make for a completely different game.
"I think that on Saturday the Scotland backs will get opportunities to really make an impact and I certainly hope so because I would say that in Stuart Hogg, Sean Maitland and Tim Visser, we probably have the most dangerous back three in many a year.
"You have got Maitland and Visser up against George North and Alex Cuthbert on the wings and then at full-back young Hogg will find himself up against Leigh Halfpenny.
"I think that whoever comes out on top of these individual battles will go a long way to booking a seat on the plane for Australia.
"I know that Warren Gatland, the Lions head coach, will be at Murrayfield for this one and if you do the business in front of him then you will give yourself a massive shot.
"But the Welsh will be keen to run the ball and have a real go after being buoyed by their two wins on the road in France and Italy. I think that could suit Scotland."
All across the field there will be match-ups that could have a big impact on the make-up of the Lions touring party.
Scotland loosehead Ryan Grant, who has become a dark horse for Australia, is up against Adam Jones in a mout-watering front row crunch.
While in the second row Richie Gray and Jim Hamilton will look to repeat the dominant line out performance that kept Scotland in a game against Ireland.
Hastings added: "Possession is going to be key on Saturday.
"If we can do that and the set piece performs to the same level it did against Ireland then we will definitely give ourselves a chance.
"But if we were to beat the Welsh that would be a significant step up from the win over the Irish.
"They have been Grand Slam champions three times in recent years and they still have a shot at the Six Nations title if they beat us."