The 2008 champion, seeded second, won 6-3 6-2 in one hour and 18 minutes at a cool and blustery Melbourne Park.
Tenth seed Makarova upset third seed Simona Halep 6-4 6-0 in Tuesday's opening match.
Rafael Nadal plays Tomas Berdych later, with Andy Murray facing Nick Kyrgios in the night session.
Sharapova, 27, took her record against Bouchard, 20, to 4-0 with a clinical performance as the Canadian made 30 errors in 78 minutes.
"I thought I had a really good start," said the Russian. "I kept my focus throughout the whole match. I didn't feel that I had too many letdowns, which is important.
"When I did have a few slips I was able to come out with great first serves or really powerful returns."
Bouchard admitted: "I felt under pressure the whole time, a bit on my back foot. That's not how I want to play. I feel like I didn't start well, and it kind of all went downhill from there."
Eugenie Bouchard won just 29% of points on her second serve compared to Maria Sharapova's 50% Jamie Murray's Australian Open came to an end with defeat in round two of the mixed doubles.
After a strong start, Murray and Taiwan's Hao-Ching Chang lost 3-6 6-4 10-5 to fourth seeds Alexander Peya and Andrea Hlavackova on court two.
"Fly high. Sing your own song." Maria Sharapova scrawls a message for the world on the camera after her win over Eugenie Bouchard.
"That's a tough question. I just want to leave it." Ekaterina Makarova is asked whether Florida-resident Maria Sharapova feels "different" to the other Russian players.
"I cannot say pressure. Just I was a little bit stressed." Simona Halep is at a loss to explain why her 'A' game deserted here.
"I don't know if I'm playing or not. Am I playing, Jill?" Eugenie Bouchard asks her agent whether she will be playing in the Fed Cup for Canada next month.
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