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NEW YORK — All victories count the same, and Roger Federer has two of them. In that sense, mission accomplished. He is through to the third round of the U.S. Open after a four-set victory (3-6, 6-2, 6-3, 6-4) over Damir Dzumhur.

But Roger Federer doesn’t usually lose sets in the early rounds at a Grand Slam. He most certainly doesn’t usually lose sets in the early rounds at a Grand Slam to players ranked well outside the top 75 in the world. Yet here we are.

For the second straight match at Arthur Ash Stadium, Federer got off to a disturbingly slow start, giving his home-away-from-home crowd a dose of nervousness they neither expected nor desired. Dzumhur, world No. 99, broke his serve twice in a row to race out to a 4-0 lead and eventually took the first set 6-3. In Federer’s first-round match on Monday, he dropped the opening set to Sumit Nagal, world No. 190.

“When it happens like this, back-to-back matches, it’s just more frustrating than anything,” he said. “Especially when the level is that low, when there are that many errors, and the energy is just kind of not there. But I can always do better, which is the great thing going forward.”

The good news for Federer: the best-of-five format in Slams makes losing the opening set jarring but not crippling, as it often is in best-of-three.

Playing with greater urgency and limiting the unforced errors, Federer asserted himself in a dominant second set (6-2) and never looked back. He was not broken the rest of the way and looked every bit a threat to win his sixth U.S. Open, dictating play from his preferred position right on the baseline. He looked comfortable off both wings and came forward early and often, winning 29 of the 43 points he came to net. Dzumhur, who came to play from the first ball, looked to his box in frustration multiple times as Federer started Federer-ing.

In the end, the gap between the 20-time Grand Slam champion and the world No. 99 was abundantly clear …in the final three sets.

The first sets, though, have recently troubled Federer. On Monday night, he dropped the opener to Nagal, a player who until then had not won a set in any ATP-level match ever. (That is something he’ll tell his grandkids: “The first set I ever won on Tour was over Roger Federer, in a night match on Arthur Ashe!). Two weeks ago in Cincinnati, he dropped the first—and second—set in losing to 21-year-old Andrey Rublev.

That’s not necessarily cause for concern. At least not yet—Federer dropped the first set of his first-round match at Wimbledon but found his form and then some, eventually winding up one point away from beating the mighty Novak Djokovic in the final. And he has time to iron out the issues before a possible—probable—semifinal with Djokovic, who had no trouble with Roberto Carballes Baena in his opening match.

Federer will get another crack at winning a first set when he faces either No. 25 seed Lucas Pouille or unseeded Dan Evans in the third round.

“I clearly have to play better from the get go,” Federer said.