"Gomez, you were brilliant!" wrote daily paper Bild on its website, adding: "First goal, first win, first hero."
But the Internet football site 11 Freunde (11 Friends) was hardly enthusiastic about the performance of Joachim Löw's side, instead philosophising that, "instead of losing beautifully, Germany won ugly."
It would seem that team coach Löw also did not seem keen to celebrate too soon. “We have to be more consistent,” he said after the match. He added that the players "have work to do up front with the tempo.”
Another daily newspaper, the Süddeutsche Zeitung, was more positive, headling its article on the victory in Lviv, Ukraine on Saturday: "Mario headers Germany into happiness."
"By heading (Sami) Khedira's cross at Portugal's near post into the back of the net, he (Gomez) set the German team free after they'd been labouring until then," the daily said.
The newspaper also reserved praise for goalkeeper Manuel Neuer for a series of vital saves before the final whistle, saying that he had "nothing less than saved the German nation."
Bild for its part gave the Bayern Munich number one its highest mark – 10/10 – as it did for defender Mats Hummels, whom it said put on an "extraordinarily classy" performance.
Football magazine Kicker also commented on Germany's workmanlike debut in the competition with a team that showed "no daring and no genius" for a good part of the match.
Germany should instead recognise that they had a good deal of luck throughout, the publication said on its website, including a 45th minute effort from Pepe that deflected down off the crossbar onto the goal-line to bounce away from danger.
Kicker also reminded fans of an interesting statistic: every time Germany has won its first match in a major competition, it has gone on to play in the final.
Löw opted to start with Gomez as his lone striker, rather than Lazio veteran Miroslav Klose, who turned 34 on Saturday, and said he was happy with the way his team opened their campaign.
"This is the start of an European championships, it's like a Formula One race without a warm-up, you have to be ready to go straight away," he said.
"Every team is very strong, it's not like a World Cup where you can acclimatise, you have to chase the game and get the three points."