The eventual victors established a 2-0 lead thanks to Bruno Vanhove's brace, but he also conceded two penalties and the teams went into the break level at 3-3.
Republic of Korea continued to battle away but missed two penalties as Belgium held on to claim the win and a place in the last eight.
A relieved Vanhove said: 'The Koreans were unlucky not to score more.'
Iran would later join Belgium in the knockout stages, topping the group with 12 points after beating Algeria 4-2. Mohamed Mokrane pulled back two goals for Algeria after Iran had taken an early 3-0 lead.
Despite bringing his personal tally up to 15 at London 2012, he said: 'I don't care about the number of goals, as long as we win.'
Algeria coach Abdelkader Khedim, meanwhile, was left in awe of the facilities at the Olympic Park, gazing around the Copper Box before saying: 'I've never seen such a beautiful room.'
World champions China also qualified for the last eight with a 3-1 win over bottom-of-the-table Canada.
Yao Yongquan scored his 11th goal of the tournament and said: 'We are confident we will win the gold medal, although we are currently number two [among the favourites].'
Today’s successful teams will discover their quarter-final opponents on Tuesday when the teams in Group A play their final matches.
If we win we said we'll shave our heads. Or at least dye our hair red, white and blue and then we'll go back to work.Jen Armbruster
In Group C of the women’s preliminary round, China secured their quarter-final place by beating Denmark 8-1. Maria Larsen was taken off with a leg injury as Karina Jorgensen scored the only goal in reply to the Chinese attack.
Chen Fengqing, who scored four goals, was eager to play down the impressive margin of victory. 'Scoring lots of goals is not what is important to us. We just want to do our best and play well,' she said.
Brazil also made it through to the last eight with a 5-4 win over Finland. The Finns took the game to the wire having drawn within a single goal, thanks to Krista Leppanen’s three penalties, with just 13 seconds left on the clock.
Brazil's Marcia Bonfim Vieira dos Santos said: 'I'm feeling very happy. It was a well deserved win. We played much better and harder and it was our dream to go through to the quarter-finals.'
Veteran Paralympian Jen Armbruster scored a hat-trick as the USA beat Australia 3-0 to reach the last eight.
The 37-year-old said: 'We're a conservative team, although, if we win we said we'll shave our heads. Or at least dye our hair red, white and blue and then we'll go back to work.
'I've been playing for 22 years. My first Paralympics was in 1992. This is my sixth. This victory has been my highlight.'
And in the final match of the evening, Amy Kneebone’s goal was enough to earn Canada a 1-0 victory over Japan.
Disappointed Japan coach Naoki Eguro said: 'The result today was regrettable because we were hoping to make it through to the quarter-finals as group winners. Very regrettable.'