Pakistan and England were eliminated after the Zimbabweans claimed two points from the washed-out game to complete the Super Six line-up with Australia, India, Sri Lanka, New Zealand and Kenya.
Pakistan scored 73 for three in the 14 overs that were bowled between bouts of rain before the match was abandoned and both sides were awarded two points.
That lifted Zimbabwe above England into third place in the group standings behind Australia and India, putting them into the second round for the second straight World Cup.
"We are elated and to get to the Super Sixes is special," Zimbabwe captain Heath Streak said. "It was a crunch game and we always knew we would have a chance."
Pakistan finished fifth in the group to be eliminated in the first round of a World Cup for the first time since 1975.
"We don't really deserve to be there," Pakistan captain Waqar Younis said. "Good luck to Zimbabwe."
Pakistan were in trouble as early as the ninth ball of the match when Saleem Elahi was trapped in front for four by medium pacer Douglas Hondo.
Rain forced the players from the field before incoming batsman Yousuf Youhana was able to take strike, and in the eighth over after the resumption he drove at a delivery from fast bowler Streak and was caught by wicketkeeper Tatenda Taibu for 17.
Saeed Anwar and Youhana accelerated Pakistan's scoring rate in their second-wicket stand of 51 runs off 56 balls.
More rain reduced the innings to 38 overs, and in the 13th Inzamam-ul-Haq hoisted a delivery from seamer Sean Ervine to deep mid-wicket for Guy Whittall to take a good running catch.
Inzamam's dismissal, for three, brought his aggregate in this World Cup to 19 runs from six innings. It also helped ease Ervine's embarrassment after he dropped Anwar on 38 in the previous over bowled by Streak.
Ervine ran from square leg to deep mid-wicket complicate what should have been a straightforward catch for Whittall, who was advancing on the dropping ball.
Another squall brought the covers back before Younis Khan had faced a ball, this time for good.
Zimbabwe finished their Group A campaign in third place with 14 points, ahead of England on 12 and Pakistan on 10. Australia ended with a maximum 24 points and India 20.