Yeovil could have taken the lead after 13 minutes when Oli Johnson was clear but he shot against goalkeeper Adam Collin's leg.
And the home side's concerns multiplied right on half-time when debutant Flavien Belson, who had been booked in the fourth minute, was shown a second yellow for another foul.
The Cumbrians seized the initiative in the second half and only the brilliance of Yeovil's new 'keeper Marek Stech, making his debut on loan from West Ham, kept them at bay until the 55th minute.
The deadlock was broken when Liam Noble picked up a right-wing cross from Tom Taiwo before blasting home from outside the box. It was all Carlisle and they doubled their advantage after 65 minutes when Nathan Jones failed to connect with a header, Jon-Paul McGovern picked up the ball and lobbed 'keeper Stech before running it into an empty net.
Danny Livesey got in on the act six minutes from time when he was on the spot to head in after a left-wing corner was flicked on.