McGovern was solicited three times in the first 12 minutes, saving alertly with his body and feet from Gomez, Mesut Ozil and Mario Goetze, who dropped into an attacking midfield role to accommodate Gomez up front.
Mueller twice went close, thrashing a shot across goal and then striking the base of the right-hand post with a plunging header, before creating the opener for Gomez.
Gomez’s subtle pass sent the Bayern Munich forward scampering through and after luring McGovern from his line, he showed great awareness to lay the ball off for Gomez, who steered the ball through a thicket of defenders and into the net.
Mueller then placed a shot against the bar from a Hector cut-back, while Gomez could only scuff meekly at McGovern when Ozil’s pass and Goetze’s dummy left him one-on-one.
All Northern Ireland offered in response was a Jamie Ward shot that went straight at Manuel Neuer, but their green-clad fans remained unbowed, volubly belting out their famous ode to flaming striker Will Grigg.
Goetze’s luck did not change in the second half as he was brilliantly thwarted again by McGovern before sliding Hector’s cross wide at the near post, and he was soon replaced by Andre Schuerrle.
Kyle Lafferty, Northern Ireland’s top scorer in qualifying, also entered the fray, replacing Conor Washington, but still Germany dominated, with McGovern again taking centre-stage.
The 31-year-old goalkeeper, who plays for Scottish club Hamilton Academical, saved one-handed from Sami Khedira’s drilled effort and then produced a superb finger-tip stop to tip away a firm header by Gomez.
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