The island archipelago, off the west coast of Africa, needed three points from their last two Group D matches to become the second smallest nation to qualify for a World Cup. However, the draw in Tripoli means they have to win at home to Eswatini on Monday.
Cape Verde moved onto 20 points, two ahead of Cameroon, who battled to win 2-0 away in Mauritius at the same time.
Cameroon's eight previous World Cup appearances are more than any other African country, but they took 57 minutes before Nicolas Ngamaleu opened the scoring, with Bryan Mbeumo adding a second in stoppage time.
Libya are third in the standings with 15 points, still chasing second place in the group, which offers the potential of a route to next year’s finals in North America through a lengthy playoff process.
Cape Verde were always going to be up against it after their Irish-born defender Roberto Lopes turned the ball into his own net in the opening minute, trying to clear a cross under pressure from striker Muad Eisa.
But the islanders came back from 3-1 down early in the second half to score twice in a dramatic finish and come close to snatching a come-from-behind victory and a place at the finals in Canada, Mexico and the US
Goalkeeping howler allowed Cape Verde back into the game
A header from Telmo Arcanjo equalised in the 29th minute, but Eisa’s mazy run three minutes from halftime set up Ezoo El Mariamy to put the home side back ahead.
Mahmoud Al Shilw then fired home a 35 metre freekick to extend the lead, but a howler had Cape Verde back in contention as Sidny Cabral made it 3-2 in the 76th minute as his long range kick went through the legs of the Libya goalkeeper Murad Al Wuheeshi.
Willy Semedo squeezed home the ball from close range for an 82nd-minute equaliser to set up a grandstand finish with another Semedo effort cleared off the line in stoppage time.
Cape Verde will still be fancied to win the group and take the automatic qualifying spot when they host the Swazis on Monday, but Eswatini served notice of their potential to cause an upset by holding Angola 2-2 on Monday.
Striker Justice Figuareido scored twice inside six minutes early in the second half as Eswatini celebrated the reopening of their national stadium, but Angola pulled two back from set pieces through Jonathan Buatu and Ary Papel.
More qualifiers are being played later on Wednesday, with Egypt and Ghana both looking to secure their World Cup spot.