Leading 4-0 in the first set, Williams let one service game go - she fell behind 15-40 and Martic converted - but the former World No.1 held all seven of her other service games easily, at the loss of just six points in fact, and she never faced another break point en route to a 62 62 triumph.
Williams has had an up-and-down year so far - finals of Auckland, first round of Australian Open - but Doha has always been one of her favorite venues. She lost early in her only previous appearance at this tournament in 2008, but she did very well the two years she played the WTA Championships here, winning the title in 2008 and making the final again in 2009 (falling to sister Serena Williams).
Awaiting Williams in the next round is the No.3 seed, Petra Kvitova, who received a first round bye this week. Kvitova leads Williams in their head-to-head series, 2-1, but all three meetings have gone to three sets - and their last encounter, at Tokyo last September, went to a third set tie-break.
Afterwards, Williams - from her Twitter for her clothing line, EleVen by Venus - called out to her many, many fans to tweet her their questions on Tuesday, which is, appropriately, the 11th of February.
? EleVen by Venus (@EleVenbyVenus) February 10, 2014