Marco Rose’s side have enjoyed a dream start to the club’s debut European season and they will be confident of securing direct passage to the last 16 after making it four victories from four, but they were made to work hard for the points in the Czech capital.

They went behind in the first half to a piece of individual brilliance by Gambian forward Ebrima Singhateh, minutes after Lewis Cook had spurned the chance to give them the lead when his penalty struck a post.

But Tobias Guddal let his team down badly when he picked up a second yellow card within two minutes of his side taking the lead.

Bournemouth had not conceded a goal on their six-game winning streak and they responded to the setback of falling behind by punishing Guddal’s error, levelling in the 57th minute when Tyler Adams smashed a loose ball into the bottom corner.

From then on there looked like being only one winner.

Evanilson’s 81st-minute effort, finished low across the goalkeeper, put them in front before Rayan added gloss with a third at the death.

The home side, under-performing this season domestically, were the better side in the opening half-an-hour, but they ought to have gone behind in the 30th minute.

Former Wolves defender Ki-Jana Hoever reached out an arm and made contact with the ball from a Bournemouth cross, but with the resulting penalty Cook hit the inside of a post and Sparta were reprieved.

Cook was at fault for the goal that gave the Czech side the lead, but there could be no accounting for the brilliance of Singhateh.

Goalkeeper Jakub Surovcik hurled the ball out quickly from a Bournemouth corner and Cook misjudged his effort to intercept, allowing Singhateh to run beyond him.

The forward’s feet to dance his way past three defenders were superb and he finished with aplomb past Michele Di Gregorio.

It was the first goal Bournemouth had conceded since being thrashed at Chelsea on October 10, but almost immediately they were given a boost, Guddal picking up a needless second yellow card for hauling down Alvaro Rodriguez.

The visitors punished the error just before the hour mark.

Rodriguez found his path to goal blocked on the edge of the area, but Sparta were unable fully to clear, the ball breaking to Adams who rifled it first time into the bottom corner.

Bournemouth were soon well on top and deserved their winning goal.

Adrien Truffert won the ball on the edge of the box, Ryan Christie took over and slipped in Evanilson, who showed wonderful feet to make space and finish into the far corner.

Substitute Rayan drilled in a third from range in the last minute.