Serbia fielded a second string team without world number two Novak Djokovic, two months after they lost to the Czech Republic in the final, and were quickly under pressure in Novi Sad.
Switzerland's Federer beat 268th-ranked Ilija Bozoljac in straight sets while Wawrinka, fresh from winning his maiden Grand Slam title at the Australian Open, eased past Dusan Lajovic in four.
Five-times champions Spain, without injured world number one Rafa Nadal and David Ferrer, got off to a poor start against Germany in Frankfurt with Davis Cup rookie Roberto Bautista Agut easily beaten by Philipp Kohlschreiber in straight sets.
The Czech Republic, who retained the Davis Cup in November, were level at 1-1 with the Netherlands in Ostrava, with Radek Stepanek going down in five tough sets to Robin Haase before Tomas Berdych thrashed Igor Sijsling in straight sets.
France got off to a flier against Australia with Jo-Wilfried Tsonga beating gutsy veteran Lleyton Hewitt in straight sets after Richard Gasquet outclassed Nick Kyrgios, also in three.
Britain lead the United States 2-0, Wimbledon champion Andy Murray having beaten John Isner's replacement Donald Young in straight sets before 175th-ranked James
Ward upset big-serving American Sam Querrey, ranked 49th, in five sets. Ward came from 1-6 7-6 3-6 down to stun a partisan US crowd at Petco Park in San Diego, winning 10 of the last 11 games as he sealed victory in three hours, 11 minutes.
Canada were level with Japan, Italy and Argentina were also all square and Kazakhstan were leading 2-0 at home to Belgium.
Switzerland go into Saturday's doubles with a commanding lead after Federer beat Bozoljac 6-4 7-5 6-2 in the opening singles before Wawrinka overcame Lajovic 6-4 4-6 6-1 7-6(7).
Federer recovered from 5-2 down in the second and having weathered the storm against hard-hitting Bozoljac, the former world number one raced through the third set to fire the Swiss ahead in the northern Serbian city of Novi Sad.
"The most important thing is that I won the match in straight sets after I struggled to read his serve early on and fought back in the second set," Federer said.
Wawrinka, who showed signs of fatigue after a long-haul flight from Melbourne following his win over world number one Nadal in the Australian Open final on Sunday, had to dig deep to fend off a spirited challenge from 23-year old Lajovic.
The young Serb squandered two set points in the fourth set tiebreak, after coming back from 3-0 down in the set and the breaker, but choked under pressure and blasted a relatively easy smash beyond the baseline as Wawrinka sealed the match.
"I always knew this was going to be a difficult match because I didn't really have time to prepare for it but I was determined to fight until the end in order to win the second point for my team," said Wawrinka.
"We are in a good position now but we have to stay focused and hopefully we will finish the job in Saturday's doubles."
Spain surrendered the first rubber as Bautista Agut lost 6-2 6-4 6-2 to Kohlschreiber but there was far more drama in the second singles with local favourite Mayer racing into a two-set lead before Lopez battled back to win the third 6-1.
The left-handed Spaniard then saved two match points in the fourth set before breaking the German to force a deciding set in front of a noisy 5,000 crowd at the Fraport Arena.
Mayer, ranked 29th, three places behind Lopez, squandered two more match points in the fifth before a thundering serve on the line put the hosts 2-0 up after almost four hours.
"I always wanted to win a singles rubber in the World Group," said Mayer in a courtside interview. "I had match points, then injured my shoulder but in that fifth set with that kind of support it worked out."
Germany's highest-ranked player Tommy Haas, the world number 12, was ruled out for the singles on Friday due to a shoulder injury but was named along with Daniel Brands to face Fernando Verdasco and Marrero in the doubles on Saturday.
The Czech Republic fought back in the defence of their title to move level at 1-1 against Netherlands after Tomas Berdych beat Sijsling 6-3 6-3 6-0 in one hour 42 minutes having earned six breaks while never allowing his opponent to come close.
The Dutch had enjoyed a fine start versus the twice defending champions when Haase fought back to beat Radek Stepanek 3-6 6-4 6-7(4) 6-2 6-1 in a titanic battle.
After an evenly-balanced affair in the opening tweo sets the pair exchanged breaks early in the third and Haase then had to save three set points to force the tiebreak but a determined Stepanek sealed it on his fifth to send the home fans wild.
However, Haase regrouped to move 2-0 in front at the start of the fourth and, with Stepanek visibly tiring, wrapped up the match with a winning forehand to the back of the court.
France's world number nine Gasquet was made to work hard for an hour by the gifted Kyrgios but the 18-year-old Australian lacked the strength to challenge his experienced opponent on the indoor clay court in Mouilleron-le-Captif, Western France.
"I was the favourite but I think (Kyrgios) has a great future ahead of him. He's going to be a top 10 player," Gasquet said after his 7-6(3) 6-2 6-2 victory.
Tsonga expected a longer fight against five-set specialist Hewitt but the world number 10 was too solid for the 32-year-old whose record on clay does not match his hard court pedigree.
Tsonga held serve throughout the match, surviving a rare scare in the fourth game of the third set by saving two break points before eventually prevailing 6-3 6-2 7-6(2).
France, who last won the trophy in 2001, have won 98 percent of their Davis Cup encounters after taking a 2-0 lead.
- Sports & Recreation
- Dusan Lajovic
- Richard Gasquet
- Ilija Bozoljac
- Czech Republic
- Feliciano Lopez
- Robin Haase
- Philipp Kohlschreiber
- Radek Stepanek
- Florian Mayer