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Gilzean, who was recently diagnosed with a brain tumour, became known as "The King of White Hart Lane" after joining Spurs in 1964.
Kenny Miller grabbed his first goal in five months as Rangers fired themselves back up to second spot with a 4-0 victory over Dundee at Ibrox.
Celtic's drive to the Ladbrokes Premiership title hit an unexpected speed bump with a goalless draw against relegation battlers Dundee at Parkhead.
Celtic moved 11 points clear of Aberdeen at the top of the Scottish Premiership with a businesslike 2-0 Boxing Day win over Dundee at Dens Park.