After a decent start at 37-0, Middlesex lost three wickets in four deliveries, with Jordan Clark dismissing Adam Rossington with the final ball of the fifth over and Reece Topley taking two in three balls at the start of the sixth.
Middlesex never really recovered from those blows, with only Luke Hollman (35*) and Eathan Bosch (31) belatedly nudging up the total with some late-order hitting.
Surrey made a stodgy start to their reply, with Noah Cornwell removing Jason Roy (the opener made two from 13 balls) and Tom Helm taking 2-24.
But with Sam Curran and Evans combining for the fifth wicket and striking nine fours and six sixes between them, Surrey were able to ease home.
