Scorers: East Stirlingshire - Glasgow (60); Stranraer - Malcolm (64), McKeown (90+1) and Turner (90+4)
Two stoppage time strikes saw Stranraer make it two wins out of two in the Betfred Cup.
John Sludden was taking charge of the visitors for the first time and East Stirlingshire were proving more than a match for Stranraer during the open period.
Home goalkeeper Max Currie had to be on his toes to deny David Grant while Scott Agnew brought a good save out of Darren Dolan at the other end.
Annan had struck the bar in the game on Saturday and the Shire repeated that trick when Connor Greene's cross deceived Currie but came back off the woodwork.
If that was a warning, the Blues failed to heed it and Sludden's men took the lead when Agnew was caught in possession and Jamie Glasgow fired home.
However, the lead was short-lived with Craig Malcolm reacting quickest to nod the ball home after first half substitute Sam McCloskey had tested Dolan with a looping header.
The game looked destined to go to penalties but there was to be late drama.
Frank McKeown popped up in stoppage time to break East Stirlingshire hearts and Kyle Turner then notched his first of the season with a picture-perfect top corner strike from 25 yards, to ensure it was six points out of six.
The Blues now face a top of the table clash with Rangers at Ibrox on Monday 25 July.
Stranraer: Currie, Robertson, Dick, McKeown, Barbour, Agnew (Turner 61), Kemp (McCloskey 25), Thomson, Gibson, Malcolm, Nade (M McGuigan 56). Not used: Osadolor, Morena and Brown.
East Stirlingshire: Dolan, Greene, Murray, A Grant, Fisher, McGregor, D McGuigan, Ure (Comrie 71), McMillan, D Grant (White 87), Glasgow (Hogg 72). Not used: Buist, Peddle and Shaw.
Referee: David Lowe Attendance: 373