Waller struck 70 off 100 balls with 14 fours and Raza made 60 off 118 with 10 fours at Harare Sports Club. At the close, Elton Chigumbura was on 40 with Shingi Masakadza on 2. (Agencies)
Waller, who got off the mark straight away with a four from off-spinner Saeed Ajmal early in second session, kept the initiative and dominated both pace and spin bowlers with ease.
Waller completed his third half century in seven tests with a four through the point region off part-time seamer Younis Khan and continued in the same vein even as debutant Raza slowly got into his groove.
They added 127 runs for fourth wicket in taking the total to 195 when Waller edged to Mohammad Hafeez at slip driving a well-flighted delivery from Ajmal, who finished with 4-77.
Pakistan-born Raza was also claimed by Ajmal as he struck the ball straight to Misbah-ul-Haq at mid-wicket a little after Waller's departure.
Ajmal then got rid of Richmond Mutumbami while Rahat Ali took out the middle stump of Prosper Utseya to end a 43-run partnership between him and Chigumbura in the second-to-last over of the day.
Earlier, opener Vusi Sibanda (31) and captain Hamilton Masakadza (19) steadied Zimbabwe with a 48-run stand after the early loss of Tino Mawoyo but their dismissals off successive deliveries undid the good work to some extent.
Sibanda was caught by wicketkeeper Adnan Akmal off pace bowler Junaid Khan in much the same way opener Mawoyo was dismissed, playing tentatively and edging an outgoing delivery.
Sibanda was out off the last ball of a Junaid Khan over and Masakadza was bowled off the first ball of the next over from Ajmal as the batsman played inside the line of a delivery and lost his off stump.
Earlier, Pakistan failed to add to its overnight score of 249-9 as Ajmal was bowled by pace bowler Tendai Chatara for 49, one short of his career-best score.
Waller struck 70 off 100 balls with 14 fours and Raza made 60 off 118 with 10 fours at Harare Sports Club. At the close, Elton Chigumbura was on 40 with Shingi Masakadza on 2.