The 36-year-old Haas produced some inspirational tennis to frustrate Wawrinka.
Berdych clawed his way back from a 6-2 5-2 deficit to stun Djokovic 2-6 7-5 6-4.
Czech Tomas Berdych tasted only his second victory in 15 clashes with Novak Djokovic to reach the semi-finals of the Rome Masters on Friday,coming from nowhere to stun the world number one 2-6 7-5 6-4 at the Foro Italico.
Nadal won his sixth title defeating the world number one 7-5 6-3 in a rain-postponed final.
Djokovic claims Rome Masters crown to stretch his unbeaten run this year to 37 matches.
Rafael Nadal opened his bid for a fifth Rome Masters title with a quick 6-1 6-3 win over Philipp Kohlschreiber on Wednesday.
World number one Roger Federer suffered a shock 2-6,6-1,7-5 defeat to the 40th ranked Ernests Gulbis.
Nadal beat Djokovic for a record fourth title in Rome.
Top seed Rafael Nadal swept aside Swede Robin Soderling at Rome Masters while Novak Djokovic and Roger Federer also had easy wins.
Andy Murray’s Rome Masters campaign floundered at the first hurdle but Rafael Nadal and Roger Federer enjoyed comfortable wins.
James Blake struggled with the windy conditions and lost to Romanian qualifier Victor Crivoi 7-5 6-3 on Monday in the first round of the Rome Masters.