The top four seeds at the Romanian Open all enjoyed comfortable wins in their first-round matches on Tuesday.
Puerta lost to Rafael Nadal in the 2005 French Open final
French Open runner-up Mariano Puerta, the tournament's top seed, beat Serbia's Janko Tipsarevic 7-5 6-2.
The Argentine was joined in round two by Filippo Volandri (No2), Andrei Pavel (No3) and Victor Hanescu (No4).
Buth fifth seed Gael Monfils failed to make it past round one, the Frenchman losing in three sets to Spaniard Albert Montanes despite taking an early lead.