Djokovic, who had lost his last two matches against Verdasco back in 2010, won the first three games en route to taking the first set, but the Spaniard fought back in the second by breaking the top-ranked Serb in the third and seventh games.
However, Djokovic again jumped out to a 3-0 lead in the decider and closed out the victory with ease.
In the women's draw, Williams won her 70th match of the year and also improved her record to 8-0 against Kirilenko.
She had to work hard for this one, though. The unseeded Russian broke Williams to take a 5-4 lead in the first set, then held three set points on her serve before Williams recovered. Kirilenko also broke Williams in the second set and took a 4-2 lead before faltering down the stretch.
"I just thought, what else can I do except fight for this point and the next point," Williams said. "Maybe I got lucky a little bit -- I just started to relax and kind of swing and not think about it too much out there. I'm obviously just really happy to get through this match today."
In another match, Serbia's Jelena Jankovic routed Spaniard Carla Suarez Navarro 6-0, 6-0.
It was only the third "double bagel" of Jankovic's career, the last one coming against another Spaniard, Virginia Ruano Pascual, in Beijing in 2007.