
Christie volleyed home from close range from a Ben Gannon-Doak cross in the seventh minute to give the hosts an early lead, and they never looked like relinquishing it.
The second half was one-way traffic and Christie doubled the Bournemouth lead when he headed home from a corner in the 69th minute, before completing his hattrick with two minutes to go through a deflected effort from the right of the box.
Rayan completed the scoring in added time to complete a job well done for Rose and to see the Cherries safely through to the fourth round of the League Cup.
Ryan Christie scored the opening goal. (Image: Richard Crease)
Rose made eight changes to his side which drew at Newcastle, as Antonio Silva, James Hill and Justin Kluivert all started again.
Michele Di Gregorio made his Cherries debut in goal, while Julio Soler and Bafode Diakite came in in defence, Lewis Cook and Ryan Christie in midfield and David Brooks, Ben Gannon-Doak and Alvaro Rodriguez in attack.
Lincoln made a good start, with much of the game played in Bournemouth’s half in the opening five minutes.
But they weren’t able to create any clear chances and the Cherries got themselves in front with an early show of their quality.
Some nice passing interplay on the right saw Brooks play a good pass out to Gannon-Doak on the left.
Ryan Christie scored the opening goal. (Image: Richard Crease)
The Scot then beat his man on the outside with a stepover and crossed for compatriot Christie to volley home at the near post with seven minutes on the clock.
Soler was not far away from applying the finishing touch to a clipped ball over the Lincoln back line, before the Imps missed a good chance.
It came from a free kick that was flicked on to Daniel Oyegoke and Di Gregorio raced out to block, it fell to Ryley Towler but he powered well over the bar.
Diakite flicked a Hill long throw towards goal but Joe Gauci was at full stretch to save, before Christie poked over the bar when he brought the ball down after a throw from Soler on the left.
Soler shot wide after making space from a corner that was cleared out to the left back.
Julio Soler (Image: Richard Crease)
Christie took aim with the final kick of the first half as he looked to find the net at the far post, but Gauci was again at full stretch to save.
Bournemouth went close in the early stages when Gannon-Doak cut in from the left and curled a shot goalwards, Rodriguez met it and tried to flick it past the diving Gauci but it went just over the bar.
Christie shot over the bar after Bournemouth won it high up the pitch, before his compatriot Gannon-Doak turned nicely and curled wide.
Rodriguez then shot over after some neat Bournemouth build up as he slipped backwards when taking aim.
Alvaro Rodriguez (Image: Richard Crease)
It was one-way traffic as the Cherries sought to put the game to bed.
Alex Toth replaced Kluivert before Hill went close after a good run and effort towards the near post, and the right back crossed well for Rodriguez but he headed just wide moments later.
Toth drew a save out of Gauci with a fiercely hit free kick from the edge of the box on the left, before the Cherries doubled their lead.
Christie completed his brace as he met Brooks’ floated corner to the back post and headed home from a tight angle.
Rose made a triple change as Rayan, Marcus Tavernier and Daniel Jebbison replaced Brooks, Gannon-Doak and Rodriguez with 13 minutes to play.
Juanlu Sanchez replaced Silva with ten minutes to go for his Cherries debut.
Ryan Christie scored a hattrick. (Image: Richard Crease)
Cook shot over the bar, before Toth dragged wide and Bournemouth confirmed their place in the fourth round with Christie’s hattrick.
A corner was played short on the right, Tavernier delivered a cross that Gauci punched out to Cook.
The midfielder then played it to Diakite who in turn fed Christie, and the Scot fired home via a deflection to rubber stamp the Cherries’ place in the next round.
And the victory was made sweeter when Jebbison fed Rayan and the Brazilian raced in on goal before finishing well to complete a comfortable 4-0 victory over Lincoln and see Bournemouth safely into the fourth round of the Carabao Cup.
AFC Bournemouth: 20, M. Di Gregorio; 6, J. Soler; 14, António Silva (booked, 60’)(Juanlu 80’); 18, B. Diakité; 5, J. Hill; 4, L. Cook (c); 10, R. Christie; 11, B. Gannon-Doak (Tavernier 77’); 19, J. Kluivert (booked, 41’)(Toth 61’); 7, D. Brooks (Rayan 77’); 30, Á. Rodríguez (Jebbison 77’).
Lincoln City: 46, J. Gauci; 20, C. Elder (booked, 27’)(Bradley 73’); 6, R. Towler; 16, D. Jefferies (booked, 48’); 33, D. Oyegoke (booked, 67’)(House 73’); 23, J. Honohan (Coubis 57’); 26, Y. Konak (Elerewe 73’); 8, T. Bayliss; 27, C. Ogbene; 11, M. Ladefoged (Street 57’); 7, R. Hackett (c).