NEW YORK >> Venus Williams needed a little pick-me-up on a rainy day in New York.

It takes more than caffeine to beat Elina Svitolina, though.

Williams had a resurgence after some coffee was sent her way after dropping the first set against the No. 5 seed, but Svitolina charged back and eventually beat Williams 6-4, 6-4 in a second-round match.

The cup of coffee was delivered from Williams’ team in the stands to a ballboy, who tried to bring it to Williams. But she walked off to the court between sets before he could get it to her, so he eventually dropped it off next to her seat.

Williams then came back to take a 3-0 lead to start the second. But having to save four break points for a tough hold in that third game seemed to take something out of the 39-year-old Williams, as Svitolina came right back to take five straight games for a 5-3 lead.

Williams then fought off five match points in a 22-point game to hold her serve before Svitolina eventually ended it on her sixth chance, improving to 13-3 in Grand Slam matches this season.

In other action, Roger Federer once again came back from a set down to advance, beating Damir Dzumhur 3-6, 6-2, 6-3, 6-4.

The second-round match was very much like the opener for the third-seeded Federer, who dropped the first set against qualifier Sumit Nagal before cruising the rest of the way. Federer again stepped up his game against the 99th-ranked Dzumhur, winning 77 percent of his first-serve points and blasting 58 winners, more than double that of his opponent.

The five-time U.S. Open champion is now 19-0 in second-round matches at Flushing Meadows and moves on to play the winner of the match between 25th-seeded Lucas Pouille and Daniel Evans.