Depay's 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 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 Alaba on the corner of the penalty area. But it was only given after referee Orel Grinfeeld consulted the pitchside VAR monitor, with Depay dispatching the spot-kick powerfully underneath the diving Daniel Bachman.
Depay had two more first-half chances, 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 teammates and the 16,000-strong crowd.
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.
Austria will secure a berth in the knockout stage if they beat Ukraine but could also qualify anyway if they end up as one of the four best third-placed teams from the six groups. The Dutch host North Macedonia on Monday safe in the knowledge they have already secured a place in the last 16.
De Bruyne leads Belgium to 2-1 comeback win over Denmark
In Group B, Kevin de Bruyne came off the bench to inspire Belgium to a 2-1 comeback win over Denmark on Thursday and a place in the Euro 2020 knockout stages on an emotional afternoon of tributes to Christian Eriksen.
Denmark got off to a dream start when Yussuf Poulsen put them ahead after 99 seconds as the team rode a wave of sentiment over playmaker Eriksen's cardiac arrest in their first game.
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Belgium's Kevin De Bruyne in action with Denmark's Christian Norgaard. (Photo: Reuters)
The Danes dominated the first half but Belgium turned to a bench bursting with talent and De Bruyne, who came on right after the interval, laid on a sublime pass for Thorgan Hazard to level in the 54th minute after a galloping run by Romelu Lukaku.
De Bruyne completed the comeback by finishing off another classy move to thump the ball into the net in the 74th minute.
Denmark never gave up and had numerous attempts to equalise, striker Martin Braithwaite hitting the bar with a header and narrowly failing to connect with a cross.
Belgium lead Group B with six points and became the second side after Italy to clinch their place in the last 16. Denmark have yet to earn a point and will need to win their final game against Russia and hope it is enough to get them through.
