Kezman could now be suspended for the beginning of the season after picking up his second booking for lashing out at Dacourt - who was also sent off in a niggly match.
It was a shame for Drogba who had scored his first goal in a Chelsea shirt, smashing home to complete the scoring after Frank Lampard's shot was only parried.
Joe Cole had opened the scoring for The Blues - trading passes with Geremi and latching onto a fine chip over the top to slot home with aplomb.
Arjen Robben then created a second for Kezman - who continued his scoring run with a straightforward finish.
Kezman had already been booked for a tussle with Francesco Totti - but he reacted furiously when Dacourt raked his foot down Robben's calf and left the referee with little choice but to red card both him and the French midfielder.
Everton also picked up an impressive win on their pre-season tour of Las Americas - crushing Mexican champions Pachuca 5-2.
James McFadden had given The Toffees an early lead and Thomas Gravesen made it two from the penalty spot.
Pachuca got back on level terms before the break - but Kevin Campbell and Kevin Kilbane both scored with headers before Nick Chadwick put a final gloss on the scoreline with the fifth.
