A controversial injury-time penalty from David Goodwillie earned Clyde victory with the last kick of the game at Shielfield on Saturday.
The spot kick was awarded in the 93rd minute when defender Robert Wilson was adjudged to have fouled Goodwillie.
The former Scotland striker, who later admitted he slipped, picked himself up and took the kick himself, but there was controversy when he appeared to stop before the kick, kicking the ball into the opposite corner after goalkeeper Robbie McCrorie had already committed himself.
But the goal was allowed to stand and secure a fourth successive win which lifted the Bully Wee above Berwick and into seventh in the table.
After a slow start Clyde started to get into their stride and McCrorie had to make three smart saves in the space of five minutes to deny Barry Cuddihy, Chris McStay and Goodwillie.
The first two were turned around for corners, with the third a block from close range.
Rangers lacked a cutting edge. Steven Thomson tried his luck from distance, Blair Currie getting down low to make the save.
Early in the second half Thomson had a free-kick which he hit straight at the keeper.
In general play was fragmented and both sides struggled to carve out opportunities.
On 77 minutes Thomson took a pass from substitute Aaron Murrell and let fly with a shot from the left side of the box, but the effort was always going high.
Mark Lamont then fired over for Clyde with a volley from a corner with only five minutes remaining and Kevin Nicholl headed narrowly wide from another corner at the back post before the dramatic ending.