Britt Assombalonga hit a second-half double - both from the penalty spot - to condemn relegation-threatened Carlisle to a nervous season finale.
Assombalonga's strike partner Conor Washington had already gone close with a third-minute effort before he opened the scoring in the 14th minute.
Defender Kgose Nthle advanced down the left to beat David Symington and his pin-point cross was steered in by Washington from 15 yards.
Graham Kavanagh's men offered little in response and Assombalonga slotted home the hosts' second from the spot in the 55th minutes after Reece Brown had been harshly adjudged to have handled Lloyd Isgrove's driven cross.
Lee Miller pulled a goal back when he fired in from 18 yards after the home defence had failed to deal with James Berrett's cross, yet Assomabalonga netted his 32nd goal of the season after being brought down in the area by Cumbrians goalkeeper Jordan Pickford.
Michael Bostwick added gloss to the scoreline in stoppage time with a deflected shot that wrong-footed Pickford.