As the offside flag went up and Jamie Vardy privately rued a rare Leicester second-half opening going begging, Bournemouth’s supporters were presented with the perfect window to take pleasure in the No 9’s misfortune. Vardy may not be as speedy as he once was but the 37-year-old was quick to respond to the jeers emanating from the corner of the ground nearest to him, twisting his head towards the travelling fans with a look of bemusement before making the 1-0 scoreline with his hands. Vardy, at it again, departed a few minutes later and ultimately had the last laugh, the teenager Facundo Buonanotte’s brilliant solo goal proving the difference.

For Steve Cooper, a welcome first Premier League win of the season. Until this, their only victory in normal time came here at home to Tranmere, a team a few places above the League Two relegation zone, in the Carabao Cup. “I feel happy for the players, equally as happy for the supporters and the staff,” Cooper said. “It was always going to be important to get that first win back in the Premier League – we’d have loved it to have been sooner.

“It’s good to get it out of the way, but I don’t think anyone was bumping into each other in the corridors saying: ‘We haven’t won.’ We have to be obsessed now about getting back-to-back wins against Southampton.”

Related: Everton v Newcastle: Premier League – live

It was far from stressless for Leicester, who survived Bournemouth twice hitting the woodwork in the second half and Evanilson seeing a headed equaliser, from Lewis Cook’s free-kick, ruled out for offside. Bournemouth surged into a three-goal lead inside 39 minutes in Monday’s victory against Southampton but here an equaliser, despite 17 shots, eluded them.

“It didn’t happen for us,” said the Bournemouth head coach Andoni Iraola, comforting himself by fiddling with the purely aesthetic plasters – for superstitious reasons – on his fingers. “You play more freely if you score straight away and you punish the opponent when you have the chances. We couldn’t take advantage of our control. We didn’t punish the opposition and if you don’t take your chances you can lose these kinds of games.”

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Buonanotte’s first-half strike was a self-made beauty. The Brighton loanee kickstarted the move a few yards inside the opposition half, playing a one-two with James Justin. Buonanotte latched on to Justin’s neat lifted pass over Milos Kerkez and after stepping inside Marcos Senesi the 19-year-old Argentinian blasted the ball into the roof of Kepa Arrizabalaga’s net. Carlos Tevez, Buonanotte’s manager at Rosario Central, once compared the way a 17-year-old Buonanotte accelerated with Lionel Messi.

Leicester’s players received a hearty applause for their efforts as they headed down the tunnel at the interval but after the restart Bournemouth ratcheted up the pressure; four minutes in, Illia Zabarnyi thumped the ground in anger after sending a header against a post from another Cook free-kick and on 72 minutes the substitute Dango Ouattara glanced a header from against the bar from a cross by another substitute, Luis Sinisterra.

In between those chances, Evanilson saw his header disallowed and another effort, on the spin, blocked by Wout Faes, and the goalkeeper Mads Hermansen saved well low down to his right from Ryan Christie.

Bournemouth peppered Leicester’s goal in the second half but Leicester came out the other end of some hairy defensive episodes and held on through five minutes of stoppage time to become the first team promoted from the Championship last season to chalk up a league victory. “There was always going to be a [nervous] edge in the second half,” Cooper said.