The Lone Star raced into a two-goal lead thanks to strikes from the Indonesia-based attacker.
Krangar took advantage of miscommunication between Black Stars central defenders John Boye and Jerry Akaminko on six minutes to slot in his first strike.
In a similar attack which was started from the right, defender Razak Nuhu failed to clear at the first attempt allowing Krangar to pounce in the box in the 9th minute.
But the Black Stars were denied the chance of taking the lead when captain Asamoah Gyan goal was ruled offside.
The first-half was played for just forty minutes which led to complains by the Black Stars players over the decision to shorten the game.
Coach Kwesi Appiah made several changes after the break to improve the chances of the Black Stars drawing level.
Isaac Coffie was replaced by Anthony Annan while Derek Boateng made way for Richmond Baokye Yiadom with Rashid Sumaila taking the place of injured John Boye.
The Black Stars lifted their game with Christian Atsu narrowly missed the target with only goalkeeper Nathaniel Sherman at his mercy after being set-up by Gyan.
The stand-in captain Gyan blasted wide before making way for Abdul Majeed Waris and Kwadwo Asamoah pile-driver could not get the consolation for the Black Stars.
The Ghanaians mounted a late siege on the Liberian goal area but that could not prevent the home side from clinching their 17th victory over the Black Stars.
Source: Ghana FA