Manchester City centre-back Nathan Ake scored twice in a little over half an hour as the Netherlands eased past 10-men Gibraltar, 200th in the FIFA rankings in Rotterdam.
Atletico Madrid forward Memphis Depay opened the scoring in the first half with a towering header before veteran Liam Walker was shown a red card the other side of the break.
The Netherlands lost in a mismatch with France on Friday in their opening Group B game.
In Group F, Sweden bounced back from a heavy opening defeat to Belgium by hammering Azerbaijan 5-0 in Solna.
Emile Forsberg, Viktor Gyokeres, Jesper Karlsson and Anthony Elanga netted for the hosts and Bahlul Mustafazade scored an own goal.
Austria avoided an upset at home to beat Estonia 2-1 despite trailing after 25 minutes from a Rauno Sappinen effort.
Cologne winger Florian Kainz opened his account for his country with 22 minutes to play before Michael Gregoritsch completed the comeback with two minutes to go.
Real Madrid’s David Alaba came off the bench after 46 minutes after Gregoritsch has missed a first half penalty.
Dominik Szoboszlai superb free-kick set Hungary on their way to a 3-0 success over Bulgaria as they started their campaign clinically.
Elsewhere in Group G, Dusan Vlahovic’s double were more than enough as Serbia beat Montenegro 2-0 in only their their third meeting since Montenegro declared independence in 2006.
In Group E, the Czech Republic were held 0-0 by lowly Moldova as Karol Swiderski scored his ninth goal in 21 internationals as Poland beat Albania 1-0 after losing to the Czechs on Friday.
On Tuesday, the pick of the ties is in Group A as Spain head to Scotland with the next international window in June.
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