The Glasgow giant hadn't lost a match since March 2020, just prior to the lockdown brought about by the coronavirus pandemic, but came unstuck at Tannadice in only the second game of the new season.
The result is likely to inject hope into the league's other sides, not least Ange Postecoglou's Celtic, which is looking to wrest back control of the domestic competition after a disappointing 2020-2021 season.
Rangers lined-up with Jon McLaughlin in goal and a back four of James Tavernier, Connor Goldson, Filip Helander and Borna Barisic as Gerrard made changes from the side that lost to Malmo in midweek.
United started brightly, but it was Rangers that had the first chance of note when Joe Aribo did well to work his way to the by-line before cutting the ball back for Alfredo Morelos, but the Colombian couldn't hit the target and the ball went over the bar.
Morelos had another chance to break the deadlock when Ryan Kent sent over a pinpoint cross from the left flank, but again, the header was wide of the target.
Dundee was far from out of the running in the first half and Peter Pawlett came close to putting the home side ahead, but couldn't quite get on the end of Logan Chalmers's superb ball into the box, and McLaughlin was bale to hold on.
Rangers continued to create half-chances in the second half, but were caught out on 64 minutes when Jamie Robson got the luck of the bounce and was able to run on unopposed to fire home and give his side a shock lead.
From that point on it was all about holding the lead for the hosts, and despite increasing pressure from Rangers, they did just that, breathing a huge sigh of relief when Goldson headed inches wide in the dying embers of the match and an even bigger one as the final whistle was blown.