The Cherries dealt out a comprehensive victory which saw goals for Steve Cook, Harry Arter and Brett Pitman, as Lee Miller's 50th-minute effort for Carlisle proved only to be a consolation.
Bournemouth's return to the second tier after an absence of 23 years was confirmed later on in the day after third-placed Brentford failed to beat lowly Hartlepool.
Hartlepool put Brentford under early pressure when Luke James scored the opening goal in the 25th minute but Marcello Trotta equalised for the Bees five minutes before the break.
However, it was not enough to stop Bournemouth, who have 82 points and are assured of a top-two finish as their nearest challengers Brentford and Doncaster meet in the final game of the season.
Doncaster could have sealed automatic promotion for themselves but they threw away the chance after losing 1-0 against Notts County.
The defeat, in which Joss Labadie scored the only goal in the 14th minute, saw Doncaster slip into second place, one point behind Bournemouth.
At the other end of the table, Scunthorpe boosted their slim chances of escaping from relegation with a 1-0 win at MK Dons.
Karl Hawley scored for the Iron in the 41st minute to leave them with a mathematical chance of avoiding the drop if they can beat Swindon, Colchester lose to Carlisle and they can engineer a three-goal swing in the last game of the season.
Portsmouth ended Sheffield United's slim chances of automatic promotion with a 3-0 victory at Fratton Park.
Shaun Cooper, David Connolly and Jed Wallace all scored in the first half to stun the Blades, but they are at least assured of a play-off place.
Joe Edwards' first-minute goal for Yeovil saw them claim a 1-0 win over Crewe, while fellow promotion hopefuls Swindon beat 10-man Stevenage 3-0.
Aden Flint opened the scoring for Swindon ahead of Stevenage striker Daniel Lopez's 39th-minute dismissal. Gary Roberts then increased Swindon's lead just after half-time before Flint added his second 17 minutes from time to complete the scoring.
Jean Yves Mvoto's last-minute goal for Oldham saw them climb their way to safety as they beat Crawley 2-1.
Matt Smith's 56th-minute strike was cancelled out by Crawley defender Mark Connolly's header midway through the second half, but Mvoto had the final word as Oldham moved clear of the bottom three.
Elsewhere, Preston beat Tranmere 1-0 thanks to Jeffrey Monakana's first-half stoppage time goal while Walsall drew 1-1 with bottom side Bury.
Febian Brandy opened the scoring for Walsall in the 22nd minute but a last-minute equaliser by Efe Sodje earned relegated Bury a point.
Meanwhile, Leyton Orient beat Coventry 1-0 thanks to Dean Cox's 45th-minute strike and Colchester drew 0-0 with Shrewsbury.