Rublev whipped through his first-round contest against Dominic Thiem 6-3 6-4 6-2 before the tournament's Extreme Heat Policy came into play as temperatures rose towards a forecast high of 36 degrees Celsius (96.8°F).
"It's super hot today so I'm super happy I was able to win in straight sets and save some energy for the next match," the fifth seed said.
"The hotter it is, the tougher it is to make the right decisions, the tougher to move. When you start to think the other guy is also feeling the same, it's a bit easier."
Fritz followed Rublev onto the John Cain Arena and, with closed roofs keeping play going on the three main showcourts, outlasted tricky Georgian Nikoloz Basilashvili 6-4 6-2 4-6 7-5.
The American eighth seed played a leading role in the United States winning the inaugural United Cup in Sydney and felt he was in a good place to make a deep run at the year's first Grand Slam.
"I don't want to put too many high expectations but I do expect a lot of myself," said the 25-year-old Californian, who next faces Tseng Chun-Hsin or local Alexei Popyrin.
"I'm in a really good spot right now, I've been playing really well, I've had a great start to the year and I'm looking to have a really big week."
Former world number two Alexander Zverev nearly lost his head in the maelstrom as he laboured against Peruvian lucky loser Juan Pablo Varillas before winning another five-setter to join Fritz and Rublev in the second round.
It was the German's first win since June, having torn ligaments in his right foot in the French Open semi-final against Rafael Nadal.
EXTREME HEAT
Women's seeds Aryna Sabalenka and Caroline Garcia enjoyed the relative cool of the earlier part of the day on Rod Laver Arena in their opening matches.
Fifth seed Sabalenka, who opened the year by winning the Adelaide International 1 title without losing a set, kept up her fine form with an emphatic 6-1 6-4 victory over Tereza Martincova.
"It wasn't that easy a match and I'm super happy to start with a win," said the Belarusian.
"I need to work on my mindset, not getting upset with every mistake I am making, I truly believe that this is the only thing that is missing in my game."
Fourth seed Garcia, who won the WTA Finals last season, was equally convincing with a 6-3 6-0 win over Canadian qualifier Katherine Sebov in just over an hour.
Garcia will next face another Canadian in 2021 U.S. Open finalist Leylah Fernandez, who came from an early break down to beat Alize Cornet 7-5 6-2 for her first win in the main draw at Melbourne Park.
In other matches that escaped the heat shutdown, Italian 21st seed Martina Trevisan went down 6-3 6-2 to qualifier Anna Karolina Schmiedlova and twice Grand Slam finalist Karolina Pliskova beat Wang Xiyu 6-1 6-3.
Men's 26th seed Miomir Kecmanovic also lost to a qualifier, beaten 6-3 6-4 7-6(3) by Nicolas Jarry in a match on Court Six concluded after play resumed.
The three-hour stoppage is likely to have an impact on the schedule but will not prevent Novak Djokovic beginning his bid for a 10th title against Spaniard Roberto Carballes Baena in the final match of the day on Rod Laver Arena.
Rublev and Sabalenka, like all Russian and Belarusian players, are competing at the tournament without national affiliation as a result of last year's invasion of Ukraine.
Tennis Australia on Tuesday morning banned fans from bringing flags of either nation into the Melbourne Park precinct after a Russian tricolour was hung on a bush next to a court where Ukrainian Kateryna Baindl was playing on Monday.
"I really thought that sport is nothing to do with politics but if everyone feels better this way feels better this way, then it's okay," said Sabalenka.
