Manchester United are clambering back to their feet. After being floored in humiliating fashion by Manchester City a month ago, they have now won five matches in a row without conceding a goal. City's swagger is becoming ever more jaunty but at least their lead at the top of the Premier League is not getting any bigger. United may not be playing with panache but they are securing points. That is something Swansea City must learn to do. If the Welsh side's finishing had matched the finesse of their buildups here, they might have secured at least a draw from this match.

Seeing City not simply emerge from United's shadow but threaten to sashay off into the distance has been disconcerting for United fans but the recent run is restoring hope. It has been built not on flair but on a doggedness that has been reinforced by the return to fitness of Nemanja Vidic and Rio Ferdinand. It is what Sir Alex Ferguson emphasised following the defeat to City and it thwarted Swansea. "[The City match] was a wake-up call," said Ferguson. "Over the years [defence] has been an integral part to our success, with the whole team defending."

Swansea forced the whole team to defend. Wayne Rooney spent much of the match in central midfield, helping Ryan Giggs and Michael Carrick, whose defensive work Ferguson hailed as "magnificent".

Swansea had come into the game with an impressive defensive record too, having conceded only one goal at home so far this season. But avoiding defeat was far from the summit of their ambition against United. Brendan Rodgers' newly promoted side have delighted with their stylish intrepidness so far this season and they were not about to change their approach for the visiting aristocrats.

They manoeuvred United on to the back foot early, with the impressive Nathan Dyer finding Danny Graham with a fine cross in the fourth minute. The striker's shot from 14 yards was charged down but Swansea recycled possession cleverly, their move culminating with a Mark Gower shot from the edge of the box that bounced wide.

That early promise was undone in the 11th minute when the right-back Angel Rangel was surprised by the vigour of United's pressing. Ryan Giggs intercepted his pass outside the hosts' area and for once Welsh fans were aghast to see Giggs dart into the box and deliver a perfect low cross. Javier Hernández flipped the ball nonchalantly into the net from close range. Rodgers refused to criticise his defender. "Blame me," said the Irishman. "He could have smashed the ball up the pitch but he just tried to play it around the corner because that's how we play, we look to pass our way out of trouble."

Swansea resumed their pretty play but United kept them at arm's length and showed that they were primed to pounce on any imprecision; Patrice Evra robbed Dyer in the 19th minute and was denied a goal by Michel Vorm, who saved his 20-yard drive.

Swansea have yet to develop such ruthlessness. They picked their way through United in the 22nd minute but, after Gower's shot was deflected, Scott Sinclair mis-hit when presented with an open goal from five yards.

Again Rodgers praised his player for at least trying to do the right thing. "Look at the ground he made up to get in that position," he said. "If he keeps doing that he'll get plenty of goals."

Shots were few but this was a high-quality spectacle that heartened because of the interplay rather than incidents.

Swansea were stronger in the second half. In the 49th minute, the substitute Joe Allen fed Sinclair, who this time made a proper connection with his shot, but David de Gea beat it away. Two minutes later Ferguson also made a substitution, withdrawing Evra, who had been given a yellow card for hacking Dyer and seemed in the sort of mood that might have led to a red. Perhaps the ongoing furore involving him and Luis Suárez has angered him or perhaps his funk was down to how well Swansea were keeping the ball.

The hosts continued to come forward after his departure. Vidic epitomised United's resilience when he dived full-length to nod away a Garry Monk header following a Swansea corner. The United captain led by example again in the 66th minute when he repelled a menacing cross from Gower after more good play by Swansea. The home crowd were becoming ever more optimistic and raucous, and United's attempts to get the second goal that might have silenced them were generally restricted to long shots from Rooney.

A fine run and cut-back by Sinclair induced more staunch defending from United, with first Fábio da Silva and then Ferdinand hurling themselves in front of shots before Ashley Williams drove wide from the edge of the area.

Swansea never did make the breakthrough and eventually tired, allowing United to control the last 10 minutes. Phil Jones might have underlined their strong finish by embellishing their lead in the last minute, but he shot against the post after a burst by Antonio Valencia. No matter, United had done enough. "They took their chance and we didn't take ours," summarised Rodgers neatly.