In another key match-up, Finland beat Poland 2-1 in a game that had a lengthy delay because of a medical emergency.
Depay scored in the ninth and 16th minutes for his 49th and 50th goals for the Netherlands at Euroborg Stadium in Groningen on Tuesday (Wednesday AEST).
In doing so he equalled the Dutch record set by team great Robin van Persie.
Depay hit 50 goals in his 102nd game for the Netherlands, while van Persie's 50th came in his 101st game in 2015.
Finland's game against Poland in Helsinki was suspended because of a medical emergency in the stadium with Finland leading 2-1. The game later resumed and the home side hung on for the win.
It was Poland's first game since star Robert Lewandowski vowed he will not play for the country again under coach Michal Probierz, who stripped the Barcelona striker of the captaincy.
It followed Lewandowski's decision not to make himself available for the game against Finland and last week's friendly against Moldova.
Finland lead Group G by a point from the Netherlands, but have played two more games. Poland dropped from first to third.
The top team in each group qualifies automatically for next year's World Cup in the US, Canada and Mexico. The second-placed team goes into play-offs.
In other World Cup qualifiers in Europe, Austria beat San Marino 4-0, Romania won 2-0 against Cyprus, Serbia beat Andorra 3-0, and Latvia and Albania fought out a 1-1 draw.
Meanwhile, Chile will miss their third straight World Cup after losing 2-0 at Bolivia on Tuesday to remain last in South America's 10-team round-robin competition.
Bolivia kept their hopes alive for an inter-continental play-off spot in a bid to reach the 2026 tournament.
The top six teams in South American qualifying secure direct berths in the World Cup. Defending champions Argentina have already qualified.
Bolivia opened the scoring through Miguel Terceros in the fifth minute and added a second in the 90th from Enzo Monteiro at the 4150-metre high El Alto Stadium, outside La Paz.
The hosts now have 17 points to put pressure on Venezuela, who have 18 and will play later at Uruguay. Both are fighting for seventh place, which secures the inter-continental play-off spot. Sixth-placed Colombia have 21 points.
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