Federer has enjoyed a fantastic 2017 so far after winning his eighth Wimbledon title in July and beating Rafael Nadal for the Australian Open at the start of the year.
And his great form has continued into the US Open with another brilliant performance against Kohlschreiber.
The 35-year-old needed five sets to progress in the first two rounds with a back injury that forced him out of the Cincinnati Masters seemingly holding him back.
But he looked back to full fitness against Feliciano Lopez in the third round.
And he continued his great form against the unseeded German.
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He swiftly made light work of the first set, breaking midway through with Kohlschreiber unable to find a way past Federer’s serve.
The 33-year-old needed to find a breakthrough in the second set but, roared on by the American crowd, Federer stormed to a two set lead.
There was slight concern at the start of the third set when Federer took a medical time out but he quickly returned to the court to continue proceedings.
Kohlschreiber played some of his best tennis in the third set but Federer was in excellent form and saw off the German by breaking his serve towards the end and holding onto his serve.
Federer will now face Juan Martin Del Potro in the quarter-finals.