NEW YORK, Sept 4 (Reuters) - After tackling two U.S. Open debutants Novak Djokovic faced an old foe on Saturday, reaching the fourth round with a 6-7(4) 6-3 6-3 6-2 win over Kei Nishikori to stay on course for a record 21st major title that would complete the calendar Grand Slam. Following first ever meetings with Denmark"s Holger Rune and Dutchman Tallon Griekspoor, Djokovic faced a seasoned campaigner in Nishikori, who was runner-up at the 2014 U.S. Open having beaten the Serb to move into that year"s final. Since then it has been one-way traffic in the rivalry with Djokovic sweeping 17 straight contests against the Japanese player, improving his head-to-head record to 18-2. But after Nishikori"s 6-2 6-0 quarter-final thumping at the hands of the world number one at the Tokyo Olympics, the 31-year-old made Djokovic sweat for his victory. Usually the headliner under the Arthur Ashe Stadium lights, Djokovic made a matinee appearance on Saturday and appeared unsettled by the conditions as he went to work under a blazing sun. A tight opening set was snatched by Nishikori in a tiebreak before Djokovic began to settle into the contest, breaking the Japanese player twice in the second on his way to levelling the match at a set apiece. In another workmanlike effort, the top seed took the decisive break in the third to go ahead 5-3 then held serve for a 2-1 lead. Now in control, Djokovic would leave Nishikori no openings to hope for a comeback, storming through the last four games of the fourth set to close out the contest in style. Djokovic now awaits the winner of the match between U.S. wildcard Jenson Brooksby and Russian Aslan Karatsev.