A thoroughly professional display from Aberdeen, that saw them encamped in the Edinburgh City half for pretty much all the 90 minutes, ended with the Dons advancing safely into the next round of the Scottish Cup.
Stephen Glass named an unchanged Aberdeen XI after Tuesday's 1-1 draw with Rangers, with the same nine men also named on the bench.
After their 2-2 draw at Kelty Hearts last weekend, there were three changes to the Edinburgh City starting line up, Lee Hamilton, James Farrell and John Robertson replacing Jack Brydon, Michael Travis and Ben Stirling, all three missing from the squad altogether.
On a lovely day for winter football, crisp, clear and without the swirling wind we've felt so much of in recent games, the Dons were smartly out of the blocks, Jonny Hayes scything a 20 yarder across the box and just inches wide of the post in the second minute.
There was a touch of the Messis from Ross McCrorie a couple of minutes later, weaving his way 60 or 70 yards forward, powering past a couple of challenges before smashing a shot at goal from the edge of the box, Schwake handling sharply under the bar.
With Aberdeen swarming forward, Ryan Hedges was next to try his luck with an effort from the edge of the box on eight minutes, Schwake down to his left to clutch the ball.
A Calvin Ramsay corner on ten minutes recalled the Breidablik game early in the season, Christian Ramirez peeling away to receive the ball on the edge of the box, his shot blocked by the massed defence.
Route one was the next line of attack, a long kick from Joe Lewis headed on by Funso Ojo, Ramirez latching onto it first time some 25 yards out, his effort flashing across goal and just wide of the post.
Hamilton was into the book on 17 minutes for a late tackle on Teddy Jenks, who needed lengthy treatment in the aftermath before he was able to resume.
The goal finally came on 22 minutes. Ojo surged forward down the left and let fly from 20 yards. Schwake did well to get down and save at his near post but Hayes was following up to pick up the pieces and square it into the six yard box, Hedges stretching to stab the ball into the net.
Lewis Ferguson wasn't far away from doubling the lead four minutes later, a 30 yard free-kick just bending away from goal. Ramsay was next to try his luck on the half hour, cutting inside and cracking a low shot into the near post, Schwake collecting well.
Hedges wasn't able to trouble the goalkeeper on 33 minutes, collecting a raking crossfield ball from Ojo before coming inside and flashing a shot over the bar. Ojo decided to take it on himself on 36, receiving a flick on from Jenks and hitting it first time from 18 yards, the ball smacking against the post.
It was 2-0 on 44 minutes, Hedges playing into Ojo and darting down the right to get the first time return pass. The Welsh international hooked the ball back into the middle and from close in, Ramirez did the rest, tucking the ball beyond Schwake.
HALF-TIME: ABERDEEN 2 EDINBURGH CITY 0
McCrorie made way at the break after feeling his hamstring late in the first half, Connor Barron coming on for his first team debut in midfield, Scott Brown dropping into centre-half. The visitors also made a change at the break, Crane replacing Robertson.
Jenks kept up the tempo with a swipe at goal on 47 minutes, Ramirez taking a whack in the face from Brian, off the ball, as the shot flew into Schwake's hands.
The Dons were massed in the Edinburgh half again, but in the early stages of the half, they were restricted to shots from some distance as City got everyone behind the ball. Declan Gallagher was the second switch for the Dons, Hedges taking a rest on the hour mark. Edinburgh responded, Hamilton making way for Reekie on 63 minutes.
Ferguson very nearly got his long range goal on 66 minutes, a free-kick from all of 35 yards flying over the wall before smashing into the woodwork, with Schwake just a bystander. Jay Emmanuel-Thomas joined proceedings on 73 minutes, Ramirez making way for him.
The Dons kept probing for that third goal and Gallagher was on the end of a Ramsay corner with 15 minutes to go, but his powerful header went straight down Schwake's throat.
Lovely play from Ojo and Emmanuel-Thomas in particular down the right almost found a goal for Barron on 78 minutes, but the massed ranks of City defenders scrambled the ball away. A minute later, a first time clip from Jenks on the half turn flew just over. Edinburgh then replaced Handling with Berry.
It should have been three on 82 minutes, a lovely pass from Emmanuel-Thomas sending Ojo away to the byline. His cut back found Emmanuel-Thomas eight yards out but with the goal gaping, he smashed his shot against the bar.
City finally had a sniff of the Aberdeen goal on 85 minutes, a ball over the top setting McDonald away, but from a tight angle, Lewis stood up and made a very good save at the near post.
Ramsay was the next in line for a shot at the visitors' goal on 87, thrashing a low effort across the face of goal and only just wide of the far post after being set up by Emmanuel-Thomas.
Finally, goal number three came two minutes into added time. Ramsay curled in a free-kick, David Bates getting just in front of the goalkeeper to head the ball back across goal, Ferguson getting up to loop a header back across goal and into the top corner.
Credit to Edinburgh who worked hard throughout, but it is the Dons who go into the draw later on Saturday night.