Swansea turned on the style in the second half to beat Birmingham 3-0 and move into second place in the Sky Bet Championship.
Kyle Naughton, Bersant Celina and Borja Baston – who celebrated his 27th birthday by becoming the division's top scorer – were on target as Birmingham's resistance crumbled after the break.
Steve Cooper, the former England Under-17 World Cup-winning coach, has had a remarkable start to his career in senior management – engineering Swansea's best opening to a campaign for 41 years.
Only Leeds' superior goal difference has prevented the Welsh side from topping the table, and Swansea have won all three league games at their Liberty Stadium fortress.
This latest victory confirmed Swansea's longest unbeaten home run – 14 games – since the 1999-2000 season when they were crowned fourth-tier champions.
Birmingham boss Pep Clotet, a familar face in Swansea from his time as Garry Monk's assistant during their Premier League days, built his gameplan on getting as many men behind the ball as possible.
It worked – just about – at 0-0, but Birmingham offered next to nothing in attack and the game was done as soon as half-time substitute Naughton lashed home after 63 minutes.
Swansea fashioned early half-chances for Yan Dhanda and Borja, while Andre Ayew eagerly went in search of his first goal in English league football since scoring for West Ham in December 2017.
Ayew met Jake Bidwell's cross with a header that Lee Camp safely gathered in the Birmingham goal, and then blazed over after controlling Matt Grimes' delightful pass on his chest.
Birmingham had a brief sight of goal when Joe Rodon – tipped to win his first Wales cap next month – carelessly conceded possession to Alvaro Gimenez.
But Rodon atoned by retreating quickly to block Lukas Jutkiewicz's effort. It was all Birmingham had to offer.
Swansea's best chance of a half which fully failed to take off came when Borja broke the offside trap and pulled the ball back to Dhanda.
But Kristian Pedersen intervened to stop the goalbound shot with his head, the defender celebrating as if he had scored at the other end.
Borja went close himself after the break when he met Grimes' free-kick to draw a wonderful acrobatic stop from Lee Camp.
But Birmingham's escape was brief as Naughton pounced seconds after Borja felt he had been pushed in the penalty area.
Naughton sized up the opportunity from 20 yards and drove home only his fourth goal in four-and-a-half years at Swansea, and his first in nearly 12 months.
Swansea doubled their lead five minutes later when Mike Van Der Hoorn outmuscled Fran Villalba and fed Celina, who smashed home from a tight angle.
Borja settled matters by rolling home his fifth goal of the season from the penalty spot, Marc Roberts' needless trip on Dhanda putting the seal on Birmingham's misery.
