With the red number showing one minute of added time, Dougie Freedman fed the ball to Howson, who slipped an inch-perfect shot inside Kieren Westwood's post for his second of the game.
In truth it was a fair reflection of a match in which the Cumbrians never soared to the dizzy heights of the first leg, where they were dominant and won 2-1.
Carlisle pressurised the visitors early on but were hit by a sucker punch from Leeds' first attack after ten minutes.
Howson played in Freedman on the wing and the veteran squared back to the onrushing youngster, who drilled the ball between two defenders leaving Westwood helpless as the ball sailed past him.
The hosts had already had a penalty appeal turned down by referee Alan Wiley, but they rarely threatened and had Westwood to thank for keeping the score down.
Jermaine Beckford should have done better with a header and Neil Kilkenny went close with a volley, before a defensive slip let in Leeds again.
Full-back Evan Horwood's awful header back to Westwood was intercepted by the dangerous Freedman, but the much sought after keeper was out in a flash to deny him.
Carlisle's Scott Dobie flashed a volley wide and Marc Bridge-Wilkinson went closer still on the stroke of half-time, but his low drive was blocked by Casper Ankergren.
Leeds dominated after the break and Beckford twice went close with long-range efforts that flew narrowly wide.
Bridge-Wilkinson was unlucky not to equalise with a clever volley on 73 minutes, but Carlisle were effectively camped in their own half.
The visitors almost grabbed a second on 78 minutes when Bradley Johnson headed against a post and with Carlisle praying for extra-time, Howson struck with seconds to play to send Leeds to Wembley.