Second seed Djokovic marked his return from a wrist injury by dismissing Radek Stepanek 6-3 7-5, while Wawrinka was a more comfortable victor over Spanish qualifier Pere Riba 6-0 6-3.
Djokovic withdrew from the Madrid Open last week due to a long-standing wrist problem but showed no lack of match fitness against the experienced Stepanek.
Wawrinka had a tough time in the Spanish capital, bowing out at the first attempt to Austrian rising star Dominic Thiem, but he bounced back in Rome to eliminate world number 98 Riba.
The Swiss will face Igor Sijsling next, after the Dutchman won through 7-6 (7-4) 7-5 against Italian wildcard Marco Cecchinato.
Spanish fifth seed David Ferrer cruised past Kazakhstan's Mikhail Kukushkin 6-1 6-2, to move into the third round with ease.
Santiago Giraldo and Ernests Gulbis both rose to a career-high ATP ranking on Monday but suffered contrasting fortunes on Tuesday.
Giraldo, of Colombia, sprung an upset by knocking out Andy Murray in Madrid last week but retired injured at 6-4 2-0 down to Croatia's Marin Cilic.
Latvia's Gulbis benefited from a withdrawal - as lucky loser Alejandro Falla was unable to complete his match, after Gulbis won the first set 6-1.
Kazakh qualifier Andrey Golubev stunned Spain's Fernando Verdasco 6-4 7-5, while South Africa's Kevin Anderson edged Canada's Vasek Pospisil 7-5 7-6 (7-4).
German 15th seed Tommy Haas was too good for local favourite Andreas Seppi 6-1 4-6 6-3.
Philipp Kohlschreiber, of Germany, upset Spanish 16th seed Tommy Robredo 6-2 6-4, while eighth seed Milos Raonic, of Canada, safely progressed past Italian wildcard Simone Bolelli 6-3 7-6 (7-5) and Russia's Dmitry Tursunov ousted Spaniard Roberto Bautista Agut 6-0 7-6 (7-4).