Everton finally managed to beat a promoted side at the third time of asking, Leon Osman's second-half winner breaking Swansea City's resistance on the ground where Queens Park Rangers won on opening day and Norwich City drew last week. The three points mean Everton leapfrog Swansea in mid-table, and it was hard to argue the Welsh side deserved anything else after setting themselves up defensively and barely managing a shot all night.

Though Swansea were a disappointment their plan almost worked, mainly due to Everton's well-documented inability to turn pressure into goals. "It was tight but we made enough chances to deserve the win," David Moyes, the Everton manager, said. "Swansea are a good team who give you a tough game, but we were in control."

For a long time it appeared the game might not be able to produce an incident worthy of note, never mind a goal. Swansea specialise in defensive organisation and keeping hold of the ball, while Everton have been struggling for goals all season. There was a contrast in styles, between Swansea's patient passing game and Everton's attempts to launch quick counters by utilising Royston Drenthe's speed or Marouane Fellaini's size, though goalmouth action was thin on the ground in the first half hour. Drenthe, quickly becoming a crowd favourite at Goodison, brings a buzz of anticipation every time he receives the ball and usually manages to do something enterprising with it, though his biggest cheer of the first half was for his persistence in tackling back to win the ball from Wayne Routledge on his own goalline.

Finally, as the interval approached and even the Swansea supporters showed signs of falling asleep, a couple of Everton chances arrived in quick succession. First Johnny Heitinga headed over from Tony Hibbert's cross, coming close to finishing a move his initial crossfield pass had started, then Drenthe cut in from the right to arrow in a cross from which Louis Saha sent a glancing header inches wide. Drenthe had started on the left but switched to the right when Seamus Coleman was forced to withdraw.

Magaye Gueye, the Everton substitute, should have opened the scoring within minutes of taking the field, but wasted an excellent Leighton Baines cutback and a clear opportunity by rolling his shot just where Michel Vorm could reach it. The goalkeeper made a good save but could only parry the shot, and Swansea had an escape when Gueye crashed the rebound against Ashley Williams's raised arm.

It would have been a harsh penalty, as Williams could not be said to have deliberately handled the ball, but when he did exactly the same thing a yard outside the area two minutes later, this time blocking an Osman shot, Kevin Friend penalised him with a free‑kick.

If it was any consolation to Everton they were the only side getting into positions to score by the end of the first half, though with Drenthe sending a shot narrowly wide from a free kick, they still needed the end result to reflect their increasing dominance. That impression threatened to change when Routledge opened the second half with Swansea's first shot on goal, Baines blocking an effort that would have been on target, and when Steven Caulker made a determined run from his own half to the edge of the Everton penalty area it began to look as if the visitors had decided to be a little bolder.

Everton weathered that miniature storm to reassert the previous pattern of making chances but not taking them. When Baines produced another inviting low cut-back from the left there was no one in the middle to meet it, and when a quickly taken free-kick briefly caught the Swansea defence off guard all Osman could manage was the meekest of toe pokes at Vorm.

However, Osman was able to make amends within moments, climbing higher than the Swansea defence to head Everton into the lead from Drenthe's corner on the hour. It was a commendable effort not only from one of the shortest players on the pitch but also from Drenthe, maker of Osman's equaliser against Norwich and whose spirited running had won the corner in the first place.

"We defended really well, so it was disappointing to concede from a corner, especially when we didn't think it actually was a corner," Brendan Rodgers said. "We'll have to keep looking for our first away win, it just means we've got to win the points we need at home."

Howard had just one Swansea effort to deal with in the rest of the game, a Danny Graham header that came straight at him. Drenthe made way for Tim Cahill 10 minutes from time and left to a standing ovation. "I thought Roy did quite well tonight," Moyes said. "There were some good bits and some not-so-good bits, but you have to accept that's the sort of player he is."