Shelly Kerr’s side came into the invitational tournament ranked ninth from 12 competing nations.
But they claimed a fifth-place finish after West Ham striker Ross’ 35th-minute strike was deflected past Katrine Abel.
Zoe Ness had come close to giving the Scots a perfect start when she rattled the crossbar early but they had to rely upon goalkeeper Jenna Fife as she pulled off a couple of important saves as Frederikke Thogersen twice threatened before the Hibs stopper bravely blocked at Nadia Nadim’s feet.
The opener went to Scotland when Jo Love’s ball over the top found Ross racing clear, with her finish ricochetting off a defender into the net.
Skipper Rachel Corsie made a vital goal-line clearance late on as she booted Nicoline Sorensen’s shot away to ensure the Scots held on for victory.
Kerr’s side will hope to maintain their momentum as they now look ahead to their opening World Cup clash with England in Nice on June 9.