Dick Advocaat's side went into the match playing catch-up following Sweden's dominant 8-0 drubbing of Luxembourg earlier in the day, leaving Netherlands needing a victory and a hatful of goals to leave themselves with a realistic chance of finishing in the top two.
The win means that they now trail second-placed Sweden by three points ahead of Tuesday's home tie against the Scandinavians, but the prospect of bridging the 12-goal gap in goal difference means that qualification is highly unlikely.
It looked as though Holland's chances would be ended this evening when Maksim Volodjko cancelled out Davy Propper's opener, but late strikes from Arjen Robben and Memphis Depay mean that they will at least go into the final matchday with a faint mathematical chance of earning a place in the playoffs.
The visitors almost took the lead midway through the first half when Vincent Janssen found space on the edge of the box before unleashing a powerful strike with minimum backlift which crashed against the crossbar with the keeper beaten.
Netherlands would not have to wait much longer for the opening goal, though, as Ryan Babel's deep cross found Robben, who in turn knocked it back for Propper to blast into the roof of the net.
Advocaat's side had won four of their last five outings coming into this match, but they struggled to add to their lead in the first half as Tonny Vilhena and Janssen both failed to make the most of presentable chances.
Janssen was again denied by goalkeeper Sergey Chernik early in the second half, before Belarus fired a warning shot when Sergey Balanovich forced Jasper Cillessen into his first serious piece of action.
It was a warning Netherlands did not heed, though, and Belarus stunned their visitors moments later when Balanovich slipped in Volodjko, who drilled an unerring finish across goal and into the bottom far corner.
Knowing that only victory would set up a straight shootout for second place with Sweden on Tuesday, Netherlands went in search of a second goal but Propper found Chernik in fine form before Bas Dost fired wide.
Aleksandar Karnitsky squandered a good chance to peg the visitors back once again in the second minute of stoppage time, being denied by a fine Cillessen save which allowed Netherlands to fight another day.
Advocaat's side were also able to reduce the goal difference deficit with a third late on as Depay got in on the act with a fine free kick in the third minute of stoppage time.
Netherlands will now host Sweden on Tuesday looking to achieve the unlikely margin of victory needed to sneak into second place in Group A, whereas Sweden only need to avoid a remarkably heavy defeat to at least make it into the playoffs.