United were at Hillsborough for their Emirates FA Cup third round replay on Tuesday night.
And the teams were met by wintry conditions as the wind blew and the snow fell as they took to the field of play, with it becoming a near blizzard almost as soon as the game kicked off.
It was the Cumbrians who showed first as patient approach play earned them a corner. The Owls struggled to deal with it and a half clearance found Ellis in space on the edge of the box. His low shot was controlled by Bennett, but another scuffed clearance found the recalled central defender unmarked and with room to shoot. He connected well but it was too close to Dawson and he scooped it up comfortably.
More good play from United brought a nice pass from Devitt which invited a cross from Liddle. That was cleared at the front post but the away side stayed on the front foot and Fox had to hook it clear before Bennett could have a go.
Wednesday enjoyed a good break when Matias used pace to make his way down the right flank. His cross was aimed at Nuhiu, but Ellis and Liddle came together to deal with the threat.
Home right back Jack Hunt got forward to support the attacking play as the game remained tight, but his cross on the run flashed across the face of goal with the strikers on their heels.
A similar delivery from Boyd followed but Liddle was glued to Nuhiu and the big forward could only guide a wayward volley over the bar.
An 18-yard free kick from a tight angle took a touch off Fox as it bent with intent towards the far post, and there was more panic in the home defence when Bennett challenged for the corner delivery. Dawson was on the floor, but so was Bennett, and it was the keeper who won the short tussle for the right to claim the ball as his own.
Boyd was a whisker away from putting his toe on a whipped through ball from Butterfield, as the game cantered from end to end, but it skipped off the surface and Bonham pulled it into his chest. That sparked a better spell for the Owls but deliveries into the area from Boyd and Hunt were well marshalled.
The home side were let off the hook when a ball over the top was flicked to Lambe following excellent control from Devitt. A lay-off to Bennett followed, as he ran into the penalty box, but he completely missed his kick and the chance to test the target was gone.
All of United's good play was made to count for nothing when they were undone by a clinical piece of route one football. A huge kick from Dawson was helped on by Nuhiu, and Matias was left to take a touch and force his way into the box. Bonham was committed and he was beaten by a clean volley which rattled into the roof of his net.
Both sides had good spells of possession following the goal and the lively Matias got behind the back line once more when a reverse pass from O'Grady put him one-on-one with Bonham. The keeper spread himself and made an excellent save.
An even better save followed when Matias turned provider with a low cross into the mix. George Boyd broke ranks to meet it and his goal-bound first-time effort was superbly stopped by one hand as Bonham dropped smartly to his right.
Carlisle spurned another good chance to cause problems when a Jones free kick looped high to the back post. Bennett had space, but he couldn't put enough on his attempt to guide it back from whence it came and it bobbled harmlessly behind.
The second period took a while to get going but quick feet from Bennett earned the Blues a corner which had Liddle interested. A touch from Fox took it away from his head and Dawson was off his line quickly to claim the second delivery.
A measured free kick from Grainger was nodded behind the advancing visitors by Ellis and Boyd broke at pace with options left and right. Grainger followed the runners to make a vital challenge just in the nick of time.
Having worked hard to stay in touch Carlisle gave another soft goal away on 66 minutes when Liddle misplaced a pass deep inside his own half. The defending side were left completely flat-footed and Matias clipped it through to Nuhiu and the centre forward dropped a shoulder and picked his spot with a curler into the bottom corner.
It became difficult for United to create any sustained forward momentum as the Owls sat on their two-goal advantage, and a high volley from Grainger summed up the frustration when he was urged to shoot by the fans behind the goal.
Jamie Devitt worked with Hope to create an opening as heavy snow descended once more, but Dawson was well positioned to move across and pull it into his midriff.
Shaun Miller was next to test Dawson with a lovely strike from distance, but the keeper got his fingertips to it to help it on its way. Two corners followed but it was home players who won the first connection and United had to pull back to try to go again.
Devitt was at the heart of the next attack as he beat his man and fed Miller on the overlap. The forward was at a tight angle and he could only find the side netting.
Bonham saved late from Matias as the offside flag went up, and he had to go low to stop a shot from the same player as the clock ticked down.
That was the last of the action as Sheffield Wednesday took their place in the fourth round and a home tie against fellow Championship outfit Reading.
Sheffield Wednesday - Matias (29), Nuhiu (66)
Sheffield Wednesday - Dawson, Hunt, Jones (Reach 79), Fox, Butterfield, Nuhiu, Matias, Boyd, O'Grady, Neilsen, Venancio. Subs - Wildsmith, Rhodes, Palmer, Joao, Wallace, Pudil.
Carlisle United - Bonham, Brown (O'Sullivan 64), Liddle, Ellis (S Miller 67), Parkes, Grainger, Lambe, Jones, Joyce, Devitt, Bennett (Hope 58). Subs - Bacon, Nabi.
Referee - Michael Salisbury
Attendance - 12,003 (932 away fans)