Defender Goldson struck in the ninth minute and added another after the break as Rangers made it two straight away league wins over Celtic for the first time in 23 years.
Celtic was without key players like striker Odsonne Edouard but few would have expected Neil Lennon's team not to register a shot on target or have a second-half attempt of any nature until the 85th minute in a miserable outing.
Steven Gerrard's men now hold a decent lead over their fierce rivals at the summit and, while Celtic still has a game in hand, Gerrard can reflect on a positive first quarter of the 2020-2021 season.
It was a dream start for Rangers when James Tavernier curled in a free-kick from the right and Goldson glanced a header into the far corner from six yards, with goalkeeper Vasilios Barkas unable to keep it out.
Celtic struggled to create many chances of note in the first half but should have been level soon after the Rangers opener.
Mohamed Elyounoussi capitalised on mistake by Goldson under a long ball, only to send his attempt high over the bar from a great opening as he attempted to lob Allan McGregor.
Having made a superb start to the first half, Rangers also struck nine minutes into the second.
Scott Arfield's deflected cross found its way to Goldson, and while the centre-back's initial effort was blocked by Shane Duffy, he composed himself to stab in a shot at the second attempt.
Celtic threw on Albian Ajeti, Leigh Griffiths and Australia's Tom Rogic from the bench, but barely troubled a Rangers backline that has only conceded three goals in 11 games.