Nicolas Pierog, Trevor Cameron and Kevan Kilistoff had a goal and an assist each for Surrey (3-0), which led 2-0 after one period and 4-0 after two en route to its 10th win in 11 preliminary round games all-time at Canada's National Junior A Championship.
Drew Best and Michael Stenerson had the other goals for the Eagles, while Adam Tambellini added two assists.
Joseph Jeanetta made 31 saves in his first start of the tournament for Minnesota (1-3), which was shut out for the first time this season.
The Eagles bombarded the Minnesota goal in the first period, outshooting the Wilderness 19-8, and took a 1-0 lead when Cameron picked up a loose puck in the slot, spun and beat Jeanetta for the game's opening goal at 13:24.
Surrey doubled its advantage before the end of the first period as Cameron tapped in a cross-ice feed from Tambellini, sending the Eagles to the dressing room up 2-0.
Best made it 3-0 at 11:20 of the second period, taking a pass from Brady Shaw and snapping a quick shot over the glove of Jeanetta. Stenerson tipped in a Devon Toews point shot with four seconds left in the middle frame to make it 4-0 Surrey after two.
Kilistoff rounded out the scoring with 4:34 left in the third period, finishing off an Eagles three-on-two break by going low to the far side past Jeanetta.
Santaguida was busiest late in the third period, as the Wilderness pushed to ruin the shutout bid. The Surrey netminder has now stopped 86 of 90 shots in his three starts, a sparkling .956 save percentage.