Germany pushed to second gear four minutes from the restart as Goretzka picked his spot to cushion home a well-timed delivery from Toni Kroos to double the lead.
Third in Group E with 11 points, Wales can secure automatic qualification for Euro 2020 with a win in its final game on Tuesday over second-place Hungary on 12 points.
Before the match there was a minute of silent in memory of Robert Enke, who committed suicide 10 years ago.
Real Madrid's Kroos then scored two fine goals to seal a comfortable win. Manuel Neuer denied Belarus a consolation from the penalty spot, tipping Ihar Stasevich's effort round the post.
A win over Northern Ireland in Frankfurt on Tuesday will guarantee Loew's new-look side first place. "Overall we did well, but at the moment I don't include us among the favourites for the European title", Kroos said.
Bruno Petkovic put Croatia ahead and Ivan Perisic rounded off the win.
Injury-hit Germany started with an unfamiliar central defensive pair of Borussia Mönchengladbach's Matthias Ginter and Freiburg's Robin Koch, the latter making only his second appearance and his first in a competitive game for Germany.
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Liverpool have been linked with England global Jadon Sancho and the last reports going on in the media are quite interesting. Nicol would like to see Sancho at Liverpool but admits a lack of game time could put the 19-year-old off.
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The man in question is Simon Wells with The Athletic stating Wells is dubbed internally as Solskjaer's "personal scout". He replied, "You know my answer". "He won the Champions League and was an incredibly good player".
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If convicted, the brothers will have to surrender all proceeds, and the five buildings the family owns in San Diego. It also noted that the alleged ringleaders, three brothers, were arrested with their wives.
"We'll see how far we've come shortly before the tournament".
Ryan Giggs's team took an early lead in Baku when Kieffer Moore headed home Harry Wilson's corner with the aid of a deflection.
Group G leaders Poland, already qualified, beat Israel 2-1 and second place Austria joined them thanks to goals from David Alaba and Stefan Lainer.
Austria secured a top-two finish in Group G with a 2-1 win over North Macedonia in Vienna.
Belgium, who have already qualified, maintained their unbeaten qualifiers run with a 4-1 win over Russian Federation, securing the top spot in Group I.
Eden and Thorgan Hazard put Roberto Martinez's side three goals ahead at the break before in-form Inter Milan striker Romelu Lukaku crashed home the fourth in the 72nd minute to make absolutely sure of the result.
Scotland defeated Cyprus 2-1 in Nicosia to move third in the same group, and Kazakhstan won 3-1 at San Marino.