Goals from Arouna Kone and Kevin Mirallas allowed Everton to see off a brave challenge from League Two battlers Dagenham & Redbridge in The Emirates FA Cup third round.
Daggers, whose relegation fears from League Two have been eased in recent weeks with back-to-back wins, were unsurprisingly second best throughout and had to thank goalkeeper Mark Cousins for keeping the score down.
Kone broke 32 minutes of resistance to head the Premier League side in front. And though Daggers held their own they rarely threatened and succumbed to defeat when Mirallas scored a late penalty.
Everton 2-0 Dagenham & Redbridge
Emirates FA Cup
Third Round Proper
Saturday 9 January
Winning club will receive £67,500
The Toffees were in total control in the opening 15 minutes and rained shots in on Cousins’ goal.
Steven Pienaar and Darron Gibson both saw efforts miss the target, while Cousins made a smart save from Mirallas.
Cousins and the Daggers defence were soon given a let-off when Aaron Lennon failed to pick out Kone with a cross, as the Ivorian lurked, waiting for a tap-in.
At the other end, the League Two club finally got a sight at goal as Joss Labadie fizzed a free-kick over the crossbar.
Ramiro Funes Mori was next to try his luck for Everton, but could find no way past the increasingly busier Cousins.
The hosts finally took the lead on 32 minutes when Bryan Oviedo whipped the ball in from the right-hand side and Kone, leading the line in place of in-form Belgium striker Romelu Lukaku, headed back across goal and beyond Cousins.
The visiting stopper had a quieter second half to endure, but kept his side in it as he denied Kone.
Daggers manager John Still threw the dice in the final quarter of the game, introducing talented teenage winger Jodi Jones and veteran striker Jamie Cureton from the bench.
With the game in the balance, Oviedo saw his shot blocked by Cousins and defender Brendan Galloway failed to turn in the loose ball.
Highlights: Everton 2-0 Dagenham & Redbridge
As the clock ticked down the 1,800-travelling Daggers fans, just 200 shy of their average home gate this season, were in good voice and sensed one chance might be enough to force an unlikely replay.
But their spirits were dampened with five minutes to go when referee Paul Tierney pointed to the penalty spot after Mirallas was tripped by Nyron Nosworthy inside the box after exchanging passes with Lennon.
And Mirallas made no mistake from 12 yards to ensure his team advanced.
With Daggers beaten, Everton began to play with a little more freedom and substitute Leon Osman struck narrowly wide.
Everton (4-4-1-1): Joel Robles; Bryan Oviedo, Phil Jagielka, Ramiro Funes Mori, Brendan Galloway; Darron Gibson, Muhamed Besic, Aaron Lennon, Steven Pienaar; Kevin Mirallas, Arouna Kone.
Substitutes: Matthew Pennington for Funes Mori 45, Leon Osman for Pienaar 77, Leandro Rodriguez for Lennon 88.
Substitutes not used: Tim Howard, Gerard Deulofeu, Ross Barkley, Conor McAleny.
Goals: Kone 32, Mirallas (pen) 85.
Dagenham & Redbridge (3-5-2): Mark Cousins; Nyron Nosworthy, Clevid Dikamona, Joe Worrall; Josh Passley, Frankie Raymond, Joss Labadie, Oliver Muldoon, Ashley Hemmings; Ashley Chambers, Christian Doidge.
Substitutes: Jodi Jones for Chambers 62, Jamie Cureton for Doidge 68, Jack Connors for Hemmings 75.
Substitutes not used: Liam O’Brien, Matt McClure, Kane Ferdinand, Joe Widdowson.
Referee: Paul Tierney