After weathering a period of Romanian pressure, the Dutch broke the deadlock courtesy of Cody Gakpo's 20th-minute effort.
The Oranje may have established an early lead, but their search for a second goal proved to be a frustrating one as chances passed them by at an alarming rate.
Stefan de Vrij headed into the side netting, Gakpo had a goal ruled out and Virgil van Dijk nodded the ball against the upright as the Romanian goal led a charmed life.
However, Romania's luck ultimately ran out in the 83rd minute when Donyell Malen tapped the ball in from Gakpo's cutback.
The Borussia Dortmund man then grabbed his second in stoppage time to ensure the Netherlands can now look forward to their first quarter-final appearance at the European Championships since 2008.
Gakpo finds crucial breakthrough
After scoring against Poland and Austria in the group stage, Gakpo required just 20 minutes of the last-16 clash to grab his third goal at Euro 2024.
The Liverpool forward collected the ball on the left flank and took a few touches before cutting inside onto his right foot to create the space for a driven near-post shot.
Romania goalkeeper Florin Nita got a hand to the powerful shot, but he could not prevent it from nestling in the back of the net.
Gakpo would have been left slightly frustrated after he saw a potential second goal ruled out in the 63rd minute due to an offside infringement.
Malen plays impact sub role
Malen dropped to the bench after making his first start of the tournament in the Netherlands' 3-2 defeat to Austria in their final group game.
However, the 25-year-old will certainly be in the conversation to start in the quarter-final following his impressive substitute performance in Munich.
Netherlands had spurned a number of glorious opportunities to add a second, before Malen produced a simple finish from Gakpo's cut-back to double his country's advantage in the 83rd minute.
After scoring his first goal at a major tournament, the Borussia Dortmund man was celebrating his second just 10 minutes later.
Malen picked up the ball on the halfway line to lead a Dutch counter-attack, before drifting inside and picking out the bottom corner with a driven finish.
A Step too far for Romania
After making a positive start to the contest, Romania spent the majority of the match on the back foot, fighting valiantly to withstand the relentless Dutch pressure.
Netherlands' extra quality ultimately told in the end, ensuring Romania's Euro 2024 campaign came to a disappointing end.
Edward Iordanescu's side finished the game with just a single shot on target, highlighting the difficulty they had in offering a threat to Bart Verbruggen's goal.
Although their journey has come to an end, the Tricolours can be proud of the fact they topped their group to make their second knockout-round appearance at the European Championships.
What next for Netherlands and Romania?
After claiming a comfortable win, the Netherlands will now turn their attention to Saturday's quarter-final, which will take place against either Turkey or Austria.
As for Romania, they will not be in action until they begin their UEFA Nations League campaign with a game against Kosovo in September