The Dutch cannot be overtaken at the head of the standings after a second win while Austria's hopes rest on the result of their last match against Ukraine.
The 11th-minute spot-kick provided an early platform for the home side and flying full back Dumfries proved a popular scorer at the Johan Cruyff Arena as he doubled the tally in the 67th minute with his second goal in as many matches.
Dumfries had netted the dramatic late winner as the Dutch edged Ukraine 3-2 on Sunday but there was less of a frenetic feel this time as they coasted through the match.
They were awarded the penalty after Dumfries was caught on the foot by Austrian captain David Alba on the corner of the penalty area. But it was only given after referee Orel Grinfeeld consulted the pitchside VAR monitor, with Depay dispatching spot-kick powerfully underneath the diving Daniel Bachman.
Depay had two more first-half chances to add to his tally, hitting the side netting with snap effort after another Alaba mistake and conjuring up a horror miss five minutes before the break.
Attack partner Wout Weghorst played a square ball in for the unmarked Depay at the back post, but he rushed the effort and skied his side-footed effort wide.
The second goal came after Donyell Malen beat the offside trap and unselfishly played in the charging Dumfries, whose finish was enthusiastically celebrated by his teammates and the 16,000-strong crowd.
"It's starting to feel like a fairytale. We are really growing, it feels good," said Dumfries.
"We controlled the game and dominated all aspects and deserved the win."
The visitors' first effort on goal came as late as the 84th minute but substitute Karim Onisiwo headed straight at home goalkeeper Maarten Stekelenburg. Without the suspended Marko Arnautovic, Austria lacked a cutting edge in attack that they will need against Ukraine on Monday.
The Dutch host North Macedonia at the same time safe in the knowledge they have already secured a place in the last 16.
"Overall I am happy with our performance. But we could have done a lot better in possession", Netherlands manager Frank De Boer told a news conference.
"We improved defensively, we didn't give away as many chances as against Ukraine. But it was frustrating how quickly we lost the ball on many occasions. We can do a lot better, but that's good, you don't want to peak too early."
The Dutch coach said he was not sure how many players would be rested for their final group match against North Macedonia on Monday, which is essentially a dead rubber as their opponents cannot progress into the next round.
"We will see who needs rest, and who wants to stay in the rhythm of playing," De Boer said. "Having five substitutions at hand certainly creates a lot of options."
Wijnaldum warned against complacency now that the first hurdle has been cleared.
"It's a bit of luxury to be through already, but we need to be aware of the temptation to relax. We have to stay focused, this team needs to work hard to get a result," he said.
Austria coach Franco said his players rarely took the game to the Dutch, and aside from a few half-chances battled to create anything in their opponent's box.
"We weren't brave enough," he told reporters. "We gave away too many balls too easily and invited them to go on the counter-attack. We created a few opportunities ourselves but were not clinical enough to finish them.
"We tried to play around and down the wings instead of penetrating the penalty-box. But the opponent played very well, they were always compact and defended well.
"Either we didn't cross or we didn't shoot. We weren't determined enough, we lacked purpose. It wasn't enough going forward."