Safin, who won the Australian Open at the start of the year, struggled from the start against his determined and highly focused opponent.
Acasuso, who beat the big Russian in their only previous meeting in the World Team Cup in 2002, edged the first set and made the crucial breakthrough in the fifth game of the second when he came to the net to earn a third break point.
Safin lost the game to trail 3-2 and began to lose his temper as he struggled to cope with Acasuso's heavy ground strokes.
The Argentine set up three match points when he caught Safin out with a delicate drop shot and won the match after the Russian netted a backhand return.
Acasuso faces a third-round contest with Swiss qualifier Stanislas Wawrinka, who beat Paradorn Srichaphan 1-6, 6-3, 7-6.
French Open champion Gaudio was in impressive form against Mantilla, giving the Spaniard no chance with his controlled ground strokes, precise passing shots and heavy serve.
The 26-year-old went 5-2 up in the second set with a stunning backhand pass and served out to love to wrap up an authoritative win. He will meet in-form Spaniard David Ferrer in the third round.
MERCILESS NADAL
Earlier, Spanish teenager Rafael Nadal issued a warning to his rivals with a merciless 6-0, 6-2 second-round destruction of Gilles Muller.
The 18-year-old, who became the youngest winner of a Masters Series event in 15 years when he beat Guillermo Coria in Monte Carlo last week, ripped through the first set in just 15 minutes.
The unseeded Muller, who hails from Luxembourg, was unable to match his opponent's powerful two-handed drives and sizzling forehands. After a brief rally in the second set, he succumbed to the in-form Spaniard.
Nadal, who is at a career-high number 11 in the rankings, faces a third-round match against Dominik Hrbaty. The Slovakian beat Italy's Potito Starace 6-3 6-2.
Coria fought off a strong challenge from big-serving Dutchman Peter Wessels to earn a 6-2, 6-7, 6-4 victory.
The fourth-seeded Argentine was joined in the third round by an improving Juan Carlos Ferrero, who eased to a 6-4, 6-4 win over Feliciano Lopez in one of the day's two all-Spanish showdowns.
Defending champion Tommy Robredo, however, went down 6-1 6-4 to fellow Spaniard Alberto Martin.
Coria looked on the verge of cracking after the towering Wessels had stormed through a tiebreak to take the second set.
The two players traded breaks at the start of the final set and Wessels broke again to take a 3-1 lead but Coria managed to compose himself and took advantage of a double fault by Wessels to level at 3-3.
The 23-year-old used his superior court craft to engineer a break point with a delicate pass in the 10th game and took the match when Wessels sent a loose backhand into the tramlines.
Coria faces a tricky third-round match against compatriot Agustin Calleri, who edged a tightly contested all-Argentine duel against Juan Ignacio Chela 6-3, 6-7, 7-6.