David Moyes' side closed February with a victory having endured four winless matches in all competitions, including a dramatic 2-2 draw with their npower League One opponents which made the Merseyside return necessary.
Goals from recalled forward Kevin Mirallas and Leon Osman came either side of a Leighton Baines penalty and, although Latics' FA Cup goal hero Matt Smith climbed off the bench to power home another towering header, the Toffees' secured a home quarter-final tie against Wigan in relative comfort.
"You go up and down through the season, I think everyone's the same," said Round. "You see that with even the boys who are right at the top.
"You don't flow impeccably all the way through the campaign. When you don't you've got to dig deep and grind out a result and then you wait for the form to come back.
"I thought we saw signs of it [last night]. It was starting to flow again and, with Kevin Mirallas coming back into some sort of form and showing what he's capable of, the signs look good."