The pair took full advantage of a docile batting strip at the Zahur Ahmed Chowdhury Stadium after South Africa won the toss and chose to bat on Tuesday, putting together a second wicket partnership of 201.
De Zorzi defied persistent cramp in the hot and humid conditions to finish the day unbeaten on 141 after reaching his century in 146 balls, while Stubbs was bowled for 106 after curtailing his usual attacking instincts and taking a measured 193 balls to get to his ton.
He was undone by a faster ball from spinner Taijul Islam that skidded on and took a bottom edge before cluttering into the stumps in the final session of the opening day.
De Zorzi had been dropped on six by debutant wicketkeeper Mahidul Islam, although it was a tough chance.
South Africa's stand-in captain Aiden Markram, who opened the batting, will feel he missed a chance to improve his Test average, setting a brisk run rate early on but then being dismissed for 33 before lunch.
He chipped the ball to mid-on off Taijul with Mominul Haque taking an easy catch.
De Zorzi will resume on Wednesday with David Bedingham, who was 18 not out when bad light brought play to an early close.
Taijul bowled a marathon 30 overs and was the pick of the bowlers, but his two wickets cost 110 runs.
South Africa are 1-0 up in the two-match series after a seven wicket win over Bangladesh in Dhaka last week.
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