Higuain clipped the ball over Rene Adler when the German goalkeeper rushed out of his goal and then scored from 30 metres to give Maradona arguably the most impressive win in his turbulent 18 months as coach.
It was the second goal in four internationals for the Real Madrid striker, who was surprisingly overlooked by Maradona and his predecessor Alfio Basile for long periods.
A frustrated German crowd watched most of the game in silence, cheered as Argentina stroked the ball around in the dying minutes and greeted the final whistle with a resounding chorus of jeers.
"We needed to show ourselves we could do what we did today," said Maradona. "We wanted to show against a good team that we are alive and we understand the moment of the Argentine national team, which has not won the World Cup for 24 years.
"We dominated in every part of the field, we cancelled out Germany's most important players and their aerial game, we took all the necessary measures," he told a news conference.
DI MARIA CLOSE
The friendly got off to a slow and sometimes scrappy start but Argentina gradually took control as they put the German defence under constant pressure, with Juan Sebastian Veron orchestrating the midfield.
The German defence often resorted to rough-arm tactics to stop Lionel Messi and Angel Di Maria, though there was nothing they could do to stop a brilliant effort by the Benfica player.
Collecting Veron's pass about 25 metres from goal, Di Maria slipped his marker, thumped his shot against the crossbar and appeared to be smacked in the face by a defender immediately afterwards.
It was no surprise when the South Americans went ahead on the stroke of halftime.
A German attack broke down and the ball was quickly played out to Higuain who broke from his own half. Adler rushed about 35 metres out of his goal but Higuain lobbed the ball over him, collected it and rolled it into the net.
Veron tried an even more spectacular effort early in the second half when Adler failed to clear the ball properly and the Estudiantes player lobbed the goalkeeper from about 40 metres only to see his effort just miss the target.
Germany came to life after Cacau replaced the ineffective Mesut Ozil in the 67th minute.
The Brazilian-born forward tested Sergio Romero with a powerful drive after being set up by a Michael Ballack backheel and volleyed over from a similar position after a one-two with Mario Gomez.
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