The Norwegian international Oyvind Leonhardsen struck in the 36th minute to seal the win, though Celtic dominated much of the second half without making it count.
Whatever the game produced was unlikely to match the emotional intensity of the ceremony beforehand, which saw the official opening of the Jock Stein stand.
In front of the "Lisbon Lions", complete with the 1967 European Cup trophy, Jean Stein, the widow of the former manager Jock, strode arm-in-arm with the present chairman, Fergus McCann, to mark the completion of the rebuilt Celtic Park. The stadium held 59,727 yesterday, but the crowd seemed to overawe the home players in a low-key first-half display.
Liverpool went ahead after 36 minutes when Karlheinz Riedle's lay-off was met by Leonhardsen ahead of the advancing Jonathan Gould, the Celtic goalkeeper, whose hesitation was punished by a crisp finish.
Celtic came closest to an equaliser after 70 minutes. Another Norwegian, Harald Brattbakk, delivered a fine 20-yard effort that struck the inside of the post and was headed to safety by Jamie Carragher.
With three minutes remaining, Michael Owen should have sealed matters for Liverpool but shot straight at Gould when clear. Leonhardsen's goal had done sufficient damage, though.
The Everton striker, Mickael Madar, could be given a three-match ban if he is reported to the Football Association for being sent off in a friendly against Fortuna Sittard in Holland last night.
The Frenchman must wait and see if the Dutch football authorities file a report to the Fottball Association, after he was shown the red card for a rash challenge during the second half of Everton's 2-0 defeat.
In the second round of the Scottish League Cup, a goal from Gregor McKechnie earned Alloa, last season's Third Division champions, an unexpected 1- 0 win at Dundee. The striker pounced eight minutes before the interval to convert a long pass from Stuart Wilson and shock the Premier League newcomers on their own Dens Park pitch.
Another Premier League outfit, Dunfermline, went down 1-0 at Second Division Livingston, now managed by the former West Ham full-back Ray Stewart. John Robertson, the former Hearts striker, struck the winner early in extra time. The Fife side's Marc Millar missed a penalty, awarded for a handling offence which earned a red card for Neil Bennett, late in normal time.Reuse content