Ghosal, the highest-ranked Indian of all-time who celebrated a best-ever world number 17 this month, defeated his 30-year-old Egyptian opponent in less than an hour, winning 11-3 11-4 2-11 11-4.
"Happy to win my match 3-1 today," Ghosal tweeted after the match.
"Aziz played some good stuff but thankfully my squash was better than yesterday!" wrote the 27-year-old from Kolkata later.
Ghosal will meet Spanish favourite Borja Golan in the semi-final of the PSA World Tour International 35 squash event in its fifth year.
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In New York, Pallikal, however, went down to world number one Nicol David of Malaysia in straight games in the quarter-final of the Carol Weymuller Open tournament.
India's number one female player Pallikal, who had defeated Australia's No.8 seed Kasey Brown yesterday to make the quarters, lost 7-11 5-11 4-11 in the Women's Squash Association Gold 50 event celebrating its 40th anniversary at The Heights Casino in Brooklyn.
"I'm tired after my long match yesterday. When you play Nicol you have to be fresh to have a chance," said Pallikal.