Streak reached his century in his 25th Test when he had Azhar Mahmood caught behind by Andy Flower for 11.
Ijaz's belligerent knock off 128 balls included 13 boundaries and a six while Yousuf amassed a sedate, Test-best 74 before fading light stopped play with four overs remaining.
The two batsmen shared a 118-run fourth-wicket stand to lift Pakistan from 92 for 3 before a mistimed pull brought an end to Ijaz's entertaining innings.
First day; Zimbabwe won toss
PAKISTAN - First innings
Saeed Anwar b Johnson 36
*Aamir Sohail c A Flower b Mbangwa 15
Ijaz Ahmad c Whittal b Mbangwa 87
Inzamamul Haq lbw b Mbangwa 19
Yousuf Youhana not out 74
Moin Khan c Mbangwa b Olonga 15
Azhar Mahmood c A Flower b Streak 11
Wasim Akram not out 0
Extras (lb5 nb10) 15
Total (for 6) 272
Fall: 1-45 2-56 3-92 4-210 5-233 6-268.
To bat: Waqar Younis, Aqib Javed, Mushtaq Ahmad.
Bowling: Streak 19-1-78-1; Olonga 14-2-43-1 (nb3); Johnson 18-2-76-1 (nb7); Mbangwa 23-9-40-3; Whittal 5-0-30-0.
ZIMBABWE: *A D R Campbell, G W Flower, N C Johnson, M W Goodwin, A Flower, C B Wishart, H H Streak, M Mbangwa, H K Olonga, G J Rennie, A R Whittal.
Umpires: Athar Zaidi (Pak) and G Sharp (Eng).