Billy Davies, the Derby County manager, insists that, given his side’s promotion to the Barclays Premier League via last season’s Coca-Cola Championship play-offs, they are two years ahead of schedule. However, in recording their first win of the season, at the expense of a previously unbeaten Newcastle United who were out of sorts last night, they do not appear, as some critics have suggested, to be light years behind the rest of the top flight.

After a 6-0 beating away to Liverpool in their previous outing, Derby showed that they were none the worse for the experience. Sam Allardyce, the Newcastle manager, expected nothing less and said: “We thought they would be fired up and expend a lot of energy closing us down. The scrap I expected, the result I didn’t.”

Allardyce cited international duty as a possible cause for the torpor of his injury-hit squad, which was without Mark Viduka, Damien Duff and Joey Barton and that had supplied 14 players to the recent round of Euro 2008 qualifying matches. That number included Michael Owen, who, feeling a twinge from the groin injury that delayed his start to the campaign, was substituted early in the second half as a precautionary measure. Allardyce insisted that the England striker will be fit for Sunday’s match at home to West Ham United.

While Owen and injuries are anything but tales of the unexpected, Allardyce was entitled to be surprised by not only the identity of the match-winner, Kenny Miller, but also the quality of the strike.

Dispatched from 30 yards into the top corner of Steve Harper’s goal, the strike ensured a memorable debut for the Scotland striker, who, in joining Derby from Celtic for £3 million, has swapped Champions League football for what is likely to be a relegation struggle. Not that, as a member of the Wolverhampton Wanderers team who lasted only a season in the top flight three years ago, he is treading unfamiliar ground.

Miller scored only four times in 25 matches during that ill-fated season, but Davies paid no heed to that when signing him. “He’s a natural finisher, has pace and ability and can make chances for others,” he said. “I’m surprised Celtic let him go. It was a superb strike and we’ll take a lot of confidence from the victory it gave us.”

The inclusion of Miller was one of four changes made by Davies to the starting lineup taken apart at Anfield. Miller was deployed alongside Steve Howard, the first player to make an attempt on goal, albeit a header from Gary Teale’s corner that looped harmlessly over Harper’s crossbar. That scenario was to be repeated twice in the second half as Derby, perhaps mindful of the fragility of their defence, attempted to put the game beyond Newcastle rather than protect their lead.

It was Newcastle, however, who should have scored first after a move begun by James Milner. His pass found Owen, who, having taken the ball around the onrushing Stephen Bywater, rolled invitingly towards the penalty spot. It was the kind of opportunity on which Owen or even his strike partner, Shola Ameobi, thrives. Unfortunately for the visiting side, Owen’s measured pass found David Rozehnal and the centre half responded with a hurried shot wide with two Derby defenders on the line.

Bywater, who earlier fielded a benign free kick from Charles N’Zogbia, was finally tested by another set-piece, this time from Gérémi. Diving to his right, Bywater palmed the ball for a corner that proved to be the precursor for a goal by Miller that was as sumptuous as it was unexpected. To make matters worse for Allardyce, the build-up owed much to the modus operandi of his former Bolton Wanderers side at their most effective.

With Newcastle claiming that they should have had a penalty as a result of the scramble from the corner, Bywater thumped the subsequent clearance deep into their half. Howard nodded the ball on and Miller, having taken a couple of steps towards Harper’s goal, fired the ball unerringly past him to send Derby’s biggest crowd - 33,016 - for five years into raptures.

More frustration followed for Allardyce as, with half-time moments away, Ameobi shot wide when well placed on the inside-right channel.

Allardyce switched to a 4-3-3 formation shortly after the restart, but, with his team increasingly devoid of ideas, only the profligacy of Howard saved them from a heavier defeat.

Derby County (4-4-2): S Bywater – T Mears, D Leacock, C Davis, A Griffin – G Teale, M Oakley, S Pearson, E Lewis (sub: J McEveley, 88min) – S Howard, K Miller (sub: B Feilhaber, 79). Substitutes not used: D Jones, R Earnshaw, A Todd. Booked: Mears, Oakley.

Newcastle United (4-4-2): S Harper – S Taylor (sub: H Beye, 76), Caçapa, D Rozehnal, C N’Zogbia – A Smith, Gérémi (sub: A Faye, 61), N Butt, J Milner – F Ameobi, M Owen (sub: O Martins, 56). Substitutes not used: S Given, M Paterson. Booked: Smith, Butt, N’Zogbia.

Referee: P Walton.