Jung was also part of the German squad that easily won the team competition, giving him two two gold medals in a single day.
After posting a dressage score that included 40.60 penalty points, Jung's trip around the cross-country course on Monday was flawless. So was his jumping effort aboard a horse named Sam.
His original score of 40.60 in the first leg of the three-event competition thus turned out to be his final one as well and that was good enough to give him first place over Sweden's Sra Algotsson Ostholt, who finished at 43.30.
Ostholt's horse Wega clipped a single fence during the final jumping ride, costing her the gold medal.
Germany's Sandra Auffarth took the bronze medal with a score of 44.80.
In the team competition, Germany wrapped up the gold medal before its last rider appeared in the jumping arena.
The Germans finished with 133.70 points while Britain took the silver medal at 138.20 and New Zealand the bronze with 144.40.