This is the first time since 2004 that the former champions, Pakistan have made it to the medal round of the competition. The Germans, meanwhile, have failed to enter the last four stage for the second successive year.
In the semifinals, Pakistan will take on Olympic Games silver medallists, The Netherlands, who posted a 2-0 win against New Zealand in the quarterfinals.
Germany took the lead in the ninth minute through veteran Moritz Fuerste, who is one of the only three players from the London Olympic winning squad in the new-look German side here.
Pakistan created a lot of openings, but were trailing by a goal at half-time.
Abbasi scored the equaliser in the 39th minute when he capitalised on an opening following the penalty corner. He was again on target in the 50th minute to put the team ahead.
But the match-winning goal was awarded only after a video referral went in Pakistan's favour.
Pakistan hung on to the lead despite some late pressure from Germany, which had a two-player advantage on the field for the last minute as Abbasi and Muhammad Waqas were shown yellow cards.
The Netherlands and New Zealand encounter was a replay of last year's bronze medal tie, as the former had won then also.
The Netherlands, who were the favourites after topping Pool B, opened the scoring in the 13th minute through a penalty corner conversion by Jeroen Hertzberger.
Billy Bakker scored in open play to increase the lead 10 minutes after half-time and then the Dutch fortified their defence to keep the Kiwi strikers at bay.
The other two semifinalists will be decided later in the day when India play Belgium and Australia take on England.