The Portuguese side made a bright start and took the lead in the sixth minute through Joao Neves, who powered home a header from Pedro Neto's cross to give his side an early advantage.
Despite dominating possession for much of the first half, Portugal struggled to create clear-cut opportunities and were punished just before the break.
DR Congo striker Yoane Wissa rose highest to head past goalkeeper Diogo Costa, scoring his country's first-ever FIFA World Cup goal and sending Congolese supporters into celebration.
The equaliser marked a historic moment for DR Congo, who are appearing at the World Cup for the first time since 1974, when the country competed under the name Zaire.
Cristiano Ronaldo, making history with his sixth World Cup appearance, found it difficult to influence the match. The veteran forward was largely quiet throughout the contest and missed two promising opportunities in the second half.
Portugal thought they had regained the lead when Joao Cancelo found the net with an overhead kick, but the goal was ruled out for offside following a review.
DR Congo continued to impress and nearly claimed all three points when experienced striker Cedric Bakambu struck the post after shrugging off pressure from Bruno Fernandes.
Portugal manager Roberto Martinez introduced fresh legs in search of a winner, but his side lacked the cutting edge needed to break down a determined Congolese defence.
The result leaves Portugal with work to do in Group K, while DR Congo celebrate a historic achievement after securing their first-ever point at the FIFA World Cup.
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