Group B leaders Tunisia controlled the vast majority of the clash in Bata, but could only muster one goal through Ahmed Akaichi.
Akaichi's improvised header capped a period of utter dominance for Georges Leekens' men that saw Yassine Chikhaoui cause all sorts of trouble for the DR Congo defence.
Tunisia looked destined to pile on the misery for the Democratic Republic and saw two goals disallowed for offside.
However, Jeremy Bokila popped up in the 66th minute to earn his side a place in the next round on goals scored with a record sixth Afcon draw in a row.
The result sees Tunisia set up a last-eight clash with hosts Equatorial Guinea in Ebebiyin, while DR Congo will face Congo in Bata.
