Manager Marco Silva made five changes to the side that started the New Year’s Day defeat to Leicester City, and it paid dividends when wingers Ademola Lookman and Bernard put the Toffees two up within 15 minutes.
But Michael Bostwick halved the deficit just before the half-hour and made for a nervy afternoon, despite the Blues ultimately getting the job done.
How did Silva’s side rate on an uneasy afternoon at Goodison?
Jordan Pickford - 6: made a fine save before Bostwick scored the rebound. Otherwise had little to do but still takes unnecessary risks with his usually excellent distribution.
Jonjoe Kenny - 6: was a willing runner all afternoon, tirelessly charging up and down the right flank. A solid if unspectacular defensive performance, but his crossing was continually erratic. Will need to show much more to convince Silva is the long-term successor to the wilting Seamus Coleman.
Kurt Zouma - 6: seemed to be troubled at times by the Imps’ similarly imposing forward, John Akinde, but besides the messy nature of Lincoln’s goal, a competent defensive display in the main from Zouma.
Yerry Mina - 6: likewise, had little to do and coped comfortably with much that came his way, though like Zouma, should have been a more commanding presence in dealing with Lincoln’s consolation. Doubtful to have dislodged Zouma or Michael Keane at the heart of central defence, though.
Leighton Baines - 8: a real throwback performance from the evergreen left-back. Now 34, Baines played as if still in his mid-twenties, darting down the left-hand side throughout and repeatedly delivering penetrative crosses, one of which set up Ademola Lookman’s headed opener. Defensively sound, too.
Tom Davies - 5: a difficult afternoon for the youngster, who was hooked at half-time for André Gomes. Didn’t impose himself enough on proceedings, and looked a soft touch against a physical Lincoln midfield.
That Silva felt he had to call for a barely-fit Gomes against opposition three leagues below Everton is a damning indictment of Davies’ performance, and indeed what his manager made of it.
Idrissa Gueye - 7: his usual industrious self, breaking up all in sight in the middle of the park. Also offered more going forward today than usual, with his passing a notable improvement on recent weeks.
Bernard - 8: edges out Baines for man of the match. The Brazilian was brilliant all afternoon, with a composed finish getting him off the mark for the first time the season. His pace and trickery were far too much for Lincoln to deal with, as Bernard toyed with their defence throughout.
Ademola Lookman - 7: a goal and another encouraging showing for Lookman, who has staked a huge claim to start against Bournemouth next Sunday. End product was not on the same level as fellow winger Bernard, but if he continues in this vein, it is surely a matter of time before ousts Theo Walcott on a regular basis.
Gylfi Sigurðsson - 6: a quieter game from Sigurdsson by his lofty standards. Never hid from the play, and tested keeper Josh Vickers in the second half with a fierce long-range effort, but certainly not his best game in a royal blue shirt.
Dominic Calvert-Lewin - 5: an underwhelming afternoon for the forward, who will have been disappointed not to score in the first half when played through on goal. His hold-up play was not at the level he knows it can be, either. Only 21 and still learning, but despite his obvious potential, he is clearly not ready to be Everton’s first-choice striker.
André Gomes - 6: certainly brighter than Davies, but if that’s the barometer by which to judge Gomes’ performance, then it is not saying much. Still looks as though he has not fully shaken off the knock sustained against Tottenham a fortnight ago - a full week without a match should do him the world of good.
Cenk Tosun - 5: another uninspiring display from the big Turk, who also should have scored from close range with his first-time effort. Still doesn’t look convincing in Silva’s more possession-orientated setup.
Richarlison - 6: certainly added the sort of verve that was previously eluding Everton in the second half, and could also have got on the score sheet, only to spurn a late opportunity. Saved the Blues with a last-gasp goal-line clearance, too.
It is difficult to complain too much about an Everton victory, but there is undoubtedly room for improvement before Bournemouth visit Goodison next Sunday.
Above all else, though, it is simply a relief to see the Blues into the fourth round draw, just as it is was to see Silva name a strong side when it could have been easier to rest the majority of his regulars.