Around the time Federer was warming up for his match with the 45th-ranked Russian, Andy Murray announced he was pulling out of the Brisbane International, while Novak Djokovic a few days earlier withdrew from his season opener in Abu Dhabi.
Rafael Nadal, Stan Wawrinka, Milos Raonic and Kei Nishikori are also under injury clouds, while world number eight Jack Sock succumbed to a hip problem earlier in the day in Perth, forcing him to retire from his singles match.
But there were no such dramas for the elder statesman Federer, who 12 months ago stunned the tennis world by ending an almost four-year Grand Slam drought with a victory at the Australian Open, after also preparing at the Hopman Cup.
The 36-year-old was too good for Khachanov, making it two straight-sets wins from as many singles matches this week as Switzerland beat Russia 3-0 in their Group B tie in front of a record Hopman Cup crowd.
Federer was stretched by Khachanov, particularly in the second set when the pair traded powerful groundstrokes.
The Russian held a set point in the tie-breaker and also saved two match points held by Federer, before the Swiss champion prevailed after Khachanov hit a forehand perilously close to the line.
It was called in by the linesman, but Federer challenged and was rewarded when replays showed the ball was out by millimetres, handing the 19-time Grand Slam champion a 6-3, 7-6 (10/8) win.
“I thought the intensity was great and the level high too,” Federer said.
“It was a good match overall and I was happy with my performance.”
The 74-ranked Belinda Bencic, on the comeback trail after injuries stalled her promising career, then upset world number 15 Anastasia Pavlyuchenkova in three sets, 6-1, 3-6, 6-3 in just under two hours to clinch the tie for the Swiss.
In the dead mixed doubles rubber, the Swiss completed a clean sweep with a three-set win under the Fast4 format.
– Pat Cash’s return –
Both Switzerland and the United States’ pairing of Sock and CoCo Vandeweghe, who beat Japan 2-1 in contentious circumstances earlier in the day, have won their opening two ties.
The victor in their clash on Thursday will advance to Saturday’s final and Federer said he expected Sock to be fit for that tie.
Sock retired early in the second set of his men’s singles clash with Japan’s Yuichi Sugita, having injured his hip during a first set tie-breaker.
The Group B tie ended with an exhibition mixed doubles match featuring the return of 52-year-old former Wimbledon champion Pat Cash to the court to team with Vanderweghe, who he coaches.
Cash also played in the inaugural Hopman Cup in 1989.
Prior to Sock’s injury, Japan’s Naomi Osaka had withdrawn from her singles match with Vandeweghe due to illness.
The end result of the injury and illness for both sides was the United States being given an intriguing 2-1 win, as Japan was ruled to have forfeited the women’s singles and mixed doubles before the Sock injury.
However, the fitness of Sock for the remainder of the tournament, and more importantly the upcoming Australian Open, was in doubt after he limped off the court.
Vandeweghe and Sock were beaten by the French team of Kristina Mladenovic and Richard Gasquet in last year’s decider.