After chief Charles Green called the current outfit the worst Gers team ever, Ally McCoist's side fall to their first defeat in front of their own fans in the Third Division
It was the Gers' first home defeat in the league, despite numerous chances and an Andrew Little goal after going two behind.
Ally McCoist made only one change from the side that beat East Stirling last week, with Northern Ireland international Dean Shiels coming in to replace David Templeton who dropped out due to injury.
Annan also made only one change, with David Murray coming into the side in place of Steven Sloan from the side that drew at home to Berwick Rangers last Saturday.
The first chance of the game came the way of the league leaders, as Lee Wallace raced down the left wing and played the ball across the penalty area for Kal Naismith, but the youngster’s strike was deflected out for a corner.
The game then raced down the other end as Anestis Argyriou tried his luck with a strike from the right-hand side, which Annan keeper Alex Mitchell had to do well in order to prevent the Gers taking the lead.
The home side suffered a blow with 33 minutes gone, as Shiels went down inside the Annan box and the forward had to be stretchered off the park, to be replaced by Barrie McKay.
Rangers should have taken the lead just before the half-hour mark, as Lee McCulloch played in Little and the forward made his way into the box, but his strike went the wrong side of Mitchell’s post and out of play.
With only two minutes gone in the second half Annan took the lead when Daniel Orsi made his way down the right wing and crossed into the box for Love to flick the ball past Alexander and into the net.
Things then went from bad to worse for the home side, as with only 10 minutes gone in the second half they found themselves two behind as Murray was given the freedom of the left wing, to cross to the back post for Hopkirk to head past Alexander.
The Ibrox side got one behind a couple of minutes later as a corner from Ian Black was headed towards goal by Francisco Sandaza and eventually headed into the net from close range by Little.
From there on it was all Rangers, as McCulloch had a couple of strikes from range that Mitchell managed to do well to save.
They continued to pepper Mitchell’s goal for the remaining minutes, with both Little and McCulloch continuing to go close but they couldn’t find an equaliser to salvage a little pride for the home side.