Berwick slumped to a disappointing home defeat at the hands of title-chasing Annan at Shielfield on Saturday.
The win, their fourth in a row, lifted the visitors to within two points of the summit, whilst Rangers were left looking over their shoulders again as Elgin closed the gap near the bottom.
Athletic were 3-0 up at half-time and a fourth goal in the second half extended their advantage before Lee Currie pulled a goal back from the penalty spot.
Annan took the lead after 19 minutes when Berwick failed to clear the ball in the box and Matthew Flynn found the net with a precise finish.
Just moments earlier, visiting goalkeeper Kenny Arthur got down well to smother a low shot from Ross Gray after being set up by Darren Lavery.
Annan doubled their advantage after 29 minutes when centre back Steven Swinglehurst got in front of his man at the near post from an Ally Love corner and found the net from close in.
Lavery then had a great chance to pull a goal back, but with the net at his mercy he shot wide from inside the box.
Josh Todd made it 0-3 after 35 minutes, neatly chipping keeper Michael Andrews from a through ball by Kenny MacKay, before firing into the empty net.
Berwick went three at the back after an hour, but just a minute later Scott Davidson crossed from the left and Todd slid the ball in at the back post to make it 0-4.
Berwick skipper Currie pulled a goal back from the penalty spot after 67 minutes, sending Arthur the wrong way after Paul Currie, in his first game back was brought down by Love.
Currie then had a chance to pull another back with a shot from only six yards out, but he was on the ground at the time and Arthur pulled off a good save.
At the other end Andrews also had to make two good saves late on to deny Annan as they tried to finish with a flourish.
Berwick: Andrews, Jacobs (Gielty 58), Hoskins, Dunlop, Fairbairn, L Currie, P Currie, Notman (Janczyk 69), Dalziel (Morris 79), Lavery, Gray
Subs:O’Brien, Morris, Gielty, Turner, Bald, Carse, Janczyk
Bookings: Fairbairn (5) foul; Notman (68) foul; Gielty 71 dissent; Hoskins 92 foul;
Annan: Arthur, Sloan, McNiff, Watson, Swinglehurst, Flynn, Davidson (Moffatt 83), Brannan, MacKay, Todd (Wood 91), Love.
Subs: Mitchell, Bradley, Anderson, Jardine, Moffatt, McCrudden, Wood
Bookings: Watson dissent 86;
Referee: Barry Cook.