First-half goals from Schuerrle, Thomas Mueller and Mario Gomez put the visitors in control of the game in Baku with the hosts briefly equalising.
Schuerrle, who made his first start since October 2015, scored his second of the evening in the 81st to give the Germans their fifth win in five qualifying matches and stretch their unbeaten run on the road in World Cup qualifiers to 44.
They are top of the group on 15 points. Group winners automatically qualify for the World Cup.
"We were at times a bit too comfortable but at the decisive moments we were there," Schuerrle told reporters. "We scored twice after the equaliser and we got the three points."
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The 26-year-old winger, who has failed to hold down a starting spot at Borussia Dortmund this season, enjoyed his rare start for Germany.
"It's all about trust. I feel very good here with the team and the coach gives me the trust I need," said Schuerrle.
The Czech Republic are second in Group C on eight points following their demolition of San Marino while Northern Ireland are a point behind and face Norway later on Sunday. Azerbaijan are also on seven.
Schuerrle made the most of his chance, tapping in after 19 minutes following good work down the wing from Jonas Hector.
Coach Joachim Loew made seven changes to the team that beat England 1-0 in their friendly earlier this week, with Julian Draxler, Gomez and Mueller in the starting lineup.
The Germans conceded their first goal of the campaign when Dmitrij Nazarov sneaked into the box and fired in the equaliser in the 30th against the run of play.
Azerbaijan's joy was short-lived, with Schuerrle pouncing on a defensive error to send Mueller through, and the attacking midfielder had no trouble rounding the keeper to put the visitors back into the driving seat in the 36th.
Gomez, who has scored in his last three league matches, headed in their third on the stroke of halftime.
The Azeris failed to mount any serious challenge in the second half with Germany content to control possession and set the pace. Schuerrle completed their win with a powerful shot from 12 metres out.
(Reporting by Karolos Grohmann; Editing by Clare Fallon)
