Everton's £6m new boy James Beattie made a winning start in the FA Cup third-round tie at Plymouth.
Beattie helped create Everton's opener for Leon Osman, who calmly chipped home from close range after 16 minutes.
And winger James McFadden doubled Everton's lead two minutes later after tricking his way into the penalty area to beat goalkeeper Romain Larrieu.
Bjarni Gudjonsson pulled a goal back for Plymouth before half-time, but Nick Chadwick sealed Everton's win late on.
Everton left out key midfield duo Thomas Gravesen and Tim Cahill - but it made little difference as they cruised into an early two-goal lead.
Osman finished well for the opener after 16 minutes, taking a deflected pass from Beattie to chip over the advancing Larrieu.
And they doubled their lead two minutes later when McFadden tricked his way through a packed penalty area to beat Larrieu.
Everton were in control, but Plymouth posted the warning signals when Lee Hodges forced goalkeeper Richard Wright to tip over the bar.
And Plymouth were back in the game after 31 minutes in bizarre cirmustances through Gudjonsson.
Everton defender Joseph Yobo had been off the field receiving treatment for a disclocated finger, and he was still regaining his position when Gudjonsson raced into the penalty to drive home a powerful finish.
Beattie marked his debut with a booking after 36 minutes when he fouled Paul Connelly, Plymouth's Liverpool-born fullback and a one time Everton season ticket holder.
And he should have scored two minutes later, but he turned Alessandro Pistone's cross over the top from inside the six-yard area as Plymouth appealed in vain for offside.
Beattie's lack of recent matches was beginning to tell, and it was no surprise when he was substituted with 20 minutes left.
Plymouth exerted pressure on Everton, but the Premiership side sealed the win when substitute Chadwick broke clear to beat Larrieu in composed fashion with six minutes left.
Plymouth boss Bobby Williamson
"I was very proud of my side.
"They worked so hard, and when you go two down like we did it does cross your mind that you could capitulate.
"But we hit back straight away and in the second half certainly created enough chances to gave got something from the game."
Everton boss David Moyes
"People might have thought that we were going to slip up. But we didn't, and I felt we defended well and got what we deserved.
"James Beattie's contribution was fine from my point of view, certainly in the first half.
"The crowd gave him a hard time, but then you expect that from a player with a price on his head and probably because he has been playing for Southampton."
Plymouth: Larrieu, Connolly, Doumbe, Coughlan, Gilbert,Capaldi, Hodges (Keith 84), Wotton, Friio, Gudjonsson, Evans.
Subs Not Used: Norris, Lasley, Adams, McCormick.
Goals: Gudjonsson 34.
Everton: Wright, Pistone, Yobo, Stubbs, Naysmith, Carsley,Osman, Kilbane, McFadden (Chadwick 79), Beattie (Cahill 71),Bent (Gravesen 79).
Subs Not Used: Weir, Turner.
Goals: Osman 16, McFadden 18, Chadwick 84.
Ref: M Messias (S Yorkshire).