The four-time champion made light work of the opening set at SW19 as she raced into a 5-0 advantage.
Shvedova managed to hold her next service game to reduce the arrears to 5-1, only for Williams to serve out to take a 1-0 lead in sets with only 26 minutes played.
Kazakhstan's Shvedova reacted positively to falling behind and she made the most of her domination by claiming a decisive break midway through the second set. The 24-year-old then kept her composure to force a deciding set thanks to a 6-4 success.
Williams booked her place in the next round after a decisive break of serve at 5-5 in the decider, which allowed her to serve out for a 7-5 triumph.