Maleeva played close to perfection in the first set, hitting devastating returns and astonishing winners almost at will to take it in just 19 minutes.
Top seed Hingis, aware that an early exit from the tournament might enable world number two Jennifer Capriati to knock her off top spot, then picked up her game and gradually wore down her opponent.
The defending champion wrapped up the match after 86 minutes with a tiring Maleeva hitting a return long on match point.
Anna Kournikova had earlier served an amazing 25 double faults in losing to Luxembourg’s Anne Kremer.
Kremer capitalised on the Russian’s mistakes to win their first round match 4-6 6-2 7-5 in one hour and 53 minutes.
It was the third time that Kournikova has lost in the first round of a tournament since she returned to action last month in Leipzig after a foot injury which has sidelined her for much of the year.
Kournikova struggled with her serve throughout the match until she bowed out by hitting a forehand into the net on match point.
Kremer now plays American Lindsay Davenport, the third seed.
First roound results:
Anne Kremer (Lux) bt Anna Kournikova (Rus) 4-6, 6-2, 7-5; Martina Hingis (Swi x1) bt Magdalena Maleeva (Bul) 0-6, 6-4, 6-2.
SHANGHAI: Top seed Monica Seles recovered from a sluggish start on Wednesday to reach the Shanghai Open quarter-finals with a 6-4 6-2 win over Japanese Saori Obata.
Seles had a difficult time finding her rhythm in the first set, spraying groundstrokes wide and double-faulting five times, twice in a row while serving at 3-2 and deuce to lose her serve.
However, the American broke back in the next game and cruised through the remainder of the second-round match.
Seventh-seeded Rita Grande of Italy also moved into the quarter-finals with a 6-2 6-4 victory over Ludmila Cervanova of Slovakia.
Taiwan’s Janet Lee also advanced to the next stage after she overpowered Rika Fujiwara of Japan 6-0 6-4. In the tournament’s final first round match, fourth-seeded Ai Sugiyama of Japan beat 20-year-old Hungarian Zsofia Gubacsi 7-5 6-2.
RESULTS (prefix number denotes seedings):
First round
4-Ai Sugiyama (Japan) beat Zsofia Gubacsi (Hungary) 7-5 6-2
Second round
Janet Lee (Taiwan) beat Rika Fujiwara (Japan) 6-0 6-4; 1-Monica Seles (United States) beat Saori Obata (Japan) 6-4 6-2; 7-Rita Grande (Italy) beat Ludmila Cervanova (Slovakia) 6-2 6-4—Reuters