The current Scottish champions won the league last season by remaining unbeaten and last lost a top flight game in March 2020 to Hamilton.
Here, the home side had the best of a goalless first half and 23-year-old defender Robson took advantage of a break of the ball in the 64th minute to score the only goal of the game.
"Over the course of 90 minutes I'm not sure we deserved to lose the game," manager Steven Gerrard said afterwards.
"But you always put yourself in that position if you don't go and score goals. Our quality and what we created today wasn't enough and whilst the game is at 0-0 you've always got that risk that if you get a couple of things wrong that goal can come.
"The result and performance is on me and the team and we have to accept that pretty quickly and move on."
Despite the long unbeaten streak, Celtic's previous success under Brendan Rodgers appears to still loom large over Scotland.
Between May 2016 and December 2017, they did not lose in 56 league games and if you add in the other domestic games the domestic record stands at 69.
And Rodgers' prediction that his side's feat may never be matched is proving right.
Rangers' loss to Dundee United was actually their second successive defeat having lost to Malmo in the first leg of their Champions League qualifier.
Gerrard is right to say they have no time to dwell on this latest loss given the second leg, at Ibrox, is on Tuesday.
"I've got belief and confidence in all of my attacking players but that's when we're at our best. Credit to Dundee United for defending well," he continued.
"When you suffer a setback, it gives you the chance to reset and give some of the players some home truths. We'll go away and analyse the game. At the moment, we've not got time to feel sorry for ourselves [with the Malmo game on Tuesday].
"We're going to need a far better level of performance to get that done."
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