Midfielder Aaron Tshibola opened the scoring in the first half at Rugby Park, with his first goal on his first start for the club.
After the break, Kris Boyd doubled the advantage with a precise finish, before Eamonn Brophy lashed in a third.
Stephen O’Donnell rounded off the scoring with a shot across Brora goalkeeper Joe Malin.
There was a sense of anticipation before this encounter, with Brora playing in the last 16 of the tournament for the first time in their history.
All the pressure was on Kilmarnock, at least according to Brora manager Ross Tokely before kick off, and he kept faith with the side that brought them to this stage of the Scottish Cup.
In contrast, Kilmarnock manager Steve Clarke made five changes from the side that beat Celtic last weekend. Among those coming in was Leo Fasan, who replaced Jamie MacDonald in the Rugby Park goal.
Another January signing, Tshibola, was also making his first start for Kilmarnock, and he opened his account as half-time approached.
There was some neat build-up play from Greg Kiltie, who then found Tshibola with a ball across the face of the goal. The midfielder showed composure to turn the ball in from close range. That 43rd minute opener put an end to the rapidly growing expectation that Brora could go in at the interval all square.
Boyd headed over after three minutes from a Kiltie free kick, while efforts from O’Donnell and Gary Dicker were well saved by Malin.
Boyd did have the ball in the back of net after 34 minutes, following some lovely play in the middle of the park by Jordan Jones to set him up, but the goal was ruled offside.
Brora started the second half in determined fashion and forced 3 well-taken corner kicks, however the second half was really all about Kilmarnock and some terrific goals.
Boyd came close to making it 2-0 as he flew in to head a corner but his effort was deflected wide. The striker did not have to wait long for his goal, though, and a delightful finish it was too. Dicker played him in and Boyd picked his spot with aplomb.
Kilmarnock brought on Brophy and he had quite an impact on the game, first forcing Malin into an excellent save with a stinging shot. But there was nothing the Brora Rangers goalkeeper could do about Brophy’s effort in the 76 minute, a rocket of a shot that flew into the net.
The home side weren’t finished there, though, and O’Donnell wrapped up the win with a fine finish from distance.
Whilst the gulf in class showed as the game progressed Brora did themselves and the Highland League proud. They were 11 Trojan’s on the park, and the defence of John Pickles, Colin Williamson, Jamie Duff and Ally MacDonald all shone on the big stage.
Brora, though, can be proud of their Scottish Cup journey, which started back in September and has seen them travel 2,000 miles. Their fans which set out from the village in a fleet of buses at 7am sang and cheered their team on and swelled the crowd up to 4278, significantly greater than the normal Premier League home gate of their hosts.
Kilmarnock manager Steve Clarke commented “It was the type of game that we expected, credit to Brora they made it really difficult for us at times. We had to be patient and eventually the chances and the goals came.
“You can get too frustrated in a game like that. We knew it was going to be difficult, Brora defended really well and worked hard, as we knew they would. We just had to keep picking away and waiting on the chance to drop. Fortunately we got one just before half-time, which made it a little easier for us in the second half. But until we got the third goal, the game was very much still alive.
We’ve kept plugging away and found a way of playing here that suits us and gets results.
A proud Brora Rangers manager Ross Tokely said, “A wee bit sad, it’s been a tremendous journey. The guys are gutted to lose four goals. I didn’t think it was a 4-0 game, although Kilmarnock were the better team. We played some good stuff and competed, which is what I asked for. I’m proud of the lads, playing against a Premiership side. You could see their class, they put on a great performance and we’ll learn from that.
The movement from Kilmarnock was excellent, they’ve got guys who are comfortable on the ball. We can learn from that, and the young lads will learn from playing against better players. We’ll come away from this much stronger as a team. I wish Kilmarnock well.
“We were massive underdogs and I told the guys to play with no pressure and fear. They could compete, no problem at all, and a lot of them would play at a higher level.”