Halep opened 2015 proceedings on Rod Laver Arena with a 6-3 6-2 defeat of Knapp in 88 minutes.
The Romanian, vying for her first grand slam title, was able to break the Italian at will, winning seven games on her return.
While she confessed to not hitting top gear, the 23-year-old said she was happy to progress.
"My forehand didn't work very well today but I'm sure next time I will play better," Halep said.
"I feel good and I'm sure I'll have my chance to win many more matches."
Lucie Hradecka: No disguising her delight. Photo / AP
Halep has set up a second-round match with Australian Jarmila Gajdosova.
Earlier, highly rated Swiss teenager Belinda Bencic became the first player eliminated from the Open, losing to German Julia Goerges.
Bencic lost 6-2 6-1 to the world No.73 on Hisense Arena, struggling to hold serve or find consistent play.
The 17-year-old was seeded for the first time at a grand slam following her run to the quarter-finals at the 2014 US Open.
But Goerges had her number, breaking the 32nd seed's serve six times en route to victory.
Two-time grand slam champion Svetlana Kuznetsova was another seed to fall on the opening day, the Russian losing 6-4 6-2 to Frenchwoman Caroline Garcia.
In other matches, China's 21st seed Peng Shuai defeated German qualifier Tatjana Maria 6-4 7-5, while Spaniard Lara Arruabarrena and Slovakia Magdalena Rybarikova also won through to the second round.
- AAP