The victory also completed a historic day for Japanese tennis with Naomi Osaka routing Ukraine's Lesia Tsurenko 6-1 6-1 and the pair became the first Japanese man and woman to reach the semi-finals of the same grand slam.
Williams first won at the US Open in 1999 and has won the tournament six times.
Serena Williams and the other U.S. Open women's semifinalists will play their matches under a closed roof.
That meant she came into the semi-final as the favourite against a player who had never before reached a Grand Slam semi-final.
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Keys and Suarez Navarro met three times previously, with Keys winning all three matches in three sets.
Osaka's first serve percentage was only 59 percent but she did not concede a point behind her first serve the entire first set and only surrendered seven points on serve over the match.
The Japanese sputtered along until earning his first break chance at 2-4 in the second set and was able to convert to get back on serve. Suarez Navarro closed to 5-3 and fought to just her second break point of the match in the ninth game, but Keys came back and after Suarez Navarro's return sailed wide she clenched her fist in celebration.
"I hate matches like this", Tsurenko said.
On creating history, Osaka added: "I just try to play one match at a time and I'm just grateful people were cheering for me".
This is the third year that the U.S. Open is being contested with a roof available at Ashe.
But he did move on, and now will face Kei Nishikori in the semifinals.
Djokovic needed two four-setters in his opening rounds but cruised through in straight sets against Richard Gasquet and John Millman. It was odd enough to see a player be allowed to do that during, instead of after, a set, but even odder for it to happen after an even number of games, rather than at an odd-game changeover.
I felt like in the first couple rounds, I was still struggling a little bit with the level. We were all sweating. I always focus every point at a time'.
The Croat rebounded to take the fourth and the rollercoaster ride continued into the fifth with Nishikori grabbing the advantage with a break at 3-1 and taking Cilic's serve again with a blistering return victor to close out victory.