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The Ballymena boxer, who is seeded eighth, had a unanimous first round win on a 29-28, 30-26, 30-27 score card.
The 27-year-old will face Tuvshinbat Byamba of Mongolia, who is a two-time Olympian, in the last 16 on Thursday 11 August (16:45 BST).
Donnelly needs two more victories to guarantee at least a bronze medal.
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After easing his way into the opening round, Donnelly looked comfortable with quick combinations and landed several punches on his Algerian opponent, all three judges scoring it 10-9 in favour of the Ballymena fighter.
His growing dominance was reflected in a second round card of 10-9, 10-9, 10-8.
Donnelly continued to pick off his opponent and eased through the third round in a comfortable start to his Olympic campaign.
Also on Sunday, Donnelly's Irish team-mate David Oliver Joyce progressed to the last 16 in the lightweight division as he earned a unanimous decision over Andrique Allisop of the Seychelles.
Joyce will face a tough next bout against Azerbaijan's number two seed Albert Selimov.
Selimov won a silver medal in the division at last year's World Championships and clinched gold in the inaugural European Games 14 months ago.
Irish welterweight Steven Donnelly won his opening bout at the Olympic Games with an emphatic victory over Algerian Zohir Kedache in Rio.