Rattie scored three times and tacked on two assists while Leipsic had two goals and three assists as Portland took a 3-1 series lead in the best-of-seven first-round matchup.
Tyler Wotherspoon had two goals and two assists for the Winterhawks, who have scored 22 combined goals in three straight wins after dropping Game 1 of the series.
Joshua Winquist scored twice for the Silvertips and Reid Petryk and Cole MacDonald had the others.
Portland's Mac Carruth picked up the win after stopping 16-of-18 shots in 50 minutes of action. Brendan Burke replaced Carruth at 9:35 of the third period and allowed two goals on five shots in relief. Everett's Austin Lotz took the loss after giving up eight goals on 29 shots before getting pulled in favour of Daniel Cotton, who turned away 6-of-9 shots in the third period.
The Winterhawks went 3 for 7 on the power play while Everett scored once on six chances with the man advantage.
Portland has the opportunity to wrap up the series on Saturday when it hosts Everett for Game 5.