The Glovers found themselves a goal down inside the opening 10 minutes as a rasping Danny Grainger strike from range broke the deadlock against the early run of play.
Looking like taking a one goal lead into the break it became 2-0 after 44 minutes courtesy of Hallam Hope as United took control.
As the game ticked towards the final 15 minutes Bevis Mugabi received a straight red card for an off the ball incident which resulted in a penalty that Grainger converted for his second of the match.
With the points ensured Shaun Miller added a fourth in stoppage time to round off an afternoon to forget for the Green and Whites.
Darren Way made one change from the side that progressed to the Emirates FA Cup second round last weekend, with Sid Nelson coming in for Jake Gray.
There were changes amongst the substitutes, however, with Jordan Green returning from a seven-game spell on the sideline alongside Jonny Maddison who had recovered from concussion.
Despite that positive news, the Green and Whites were left a man light on the bench in Cumbria with Ryan Dickson dropping out late on due to illness.
After a 330-mile trip to Carlisle the visitors showed no signs of lethargy, starting on the front foot and engineering a glorious chance to open the scoring after just four minutes.
Rhys Browne’s positive run through the middle was rewarded with a lucky ricochet which set Sam Surridge through on goal, only for the outstretched leg of Jack Bonham to stop the Town striker as he looked to round the home ‘keeper.
That chance came after Otis Khan was unusually found lacking a final ball after breaking to the by-line in the opening exchanges, before United issued a sucker punch.
With seven minutes on the clock, the Cumbrians put together their first meaningful attack and came away with the opener.
Captain Grainger found too much space 25 yards from goal and picked out the top corner with a shot that would’ve beaten any goalkeeper.
Boasting the lead, Carlisle could bide their time in an attacking sense and get numbers behind the ball in defence, meaning the half petered out until the final five minutes.
After half-an-hour of little action, the game burst into life once again as Artur Krysiak was perfectly placed to tip Shaun Miller’s well-hit strike over the bar from inside the box.
That opportunity roused the home crowd and they were on the feat as the game ticked into the 44th minute.
Good work from Miller wide on the right allowed the substitute to cut the ball back for Hope who directed the ball into the far corner with an inch-perfect first-time shot.
Despite a promising start from the Glovers, Way’s side trudged into the break two goals down and in need of a dramatic second-half performance.
In order to try and achieve that, Gray and Green were introduced for Tom James and Rhys Browne as the visitors switched to 4-4-2.
Mirroring the first period, chances came straight after the restart as firstly Hope had a shot from range tipped round the post by Krysiak before an immediate chance at the other end.
Gray beat goal scorer Grainger wide on the right and weaved into the box, only for his shot to lack the required power to beat Bonham.
Mimicking the opening 45 minutes by becoming a flat affair in the middle of half, the encounter burst back into life with 72 minutes played.
Green went in the referee’s book for a late foul only for Mugabi to be given his marching orders moments later for an altercation missed by virtually all inside the ground bar the officials.
Adding insult to injury a spot kick was awarded as further punishment giving Carlisle’s captain the platform to double his personal tally and ensure all three points.
With the result a formality, Miller added a fourth in stoppage time to end a four-game unbeaten streak for Town, as Way’s side continue to look for a consistent winning formula on their travels.
Carlisle United: Bonham; Brown, Liddle, Hill, Grainger; Lambe (O’Sullivan 81’), Joyce, Jones, Adams (Miller 28’); Hope (Etuhu 81’), Bennett.
Subs not used: George, Miller, Parkes, Cosgrove.
Yeovil Town: Krysiak; Sowunmi, Nelson, N. Smith; Mugabi, Worthington, Bailey, James; Browne (Green 45’), Surridge, Khan.
Bookings: Browne 30’, Green 72’, Mugabi (73’ red)
Subs not used: Maddison, Davies, C. Smith, Santos.