They traded service holds through the second set until the final game when Tomic's eighth double fault sealed Ferrer's comprehensive win.
"All tennis players have pressure, but at this moment of my career, I need to enjoy these types of matches on Centre Court," Ferrer said.
"I am 34 years old, 35 next month, so I hope I will play a little bit longer," added the Spaniard who faces another Australian, wildcard Jordan Thompson, in the second round.
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Nicolas Mahut staged a brilliant comeback against Stephane Robert to win the all-French contest 4-6 6-3 6-4. He will meet the winner of the clash between seventh seed Grigor Dimitrov and Steve Johnson.
In the women's event, fourth seed Garbine Muguruza staved off Samantha Stosur's spirited comeback, prevailing 7-5 6-7(2) 7-5 in a three-hour battle that ended in disappointment for the partisan crowd.
The 2016 French Open champion saved three set points to surge ahead and broke Stosur twice early in the second set.
Stosur mounted a strong reply, racing into a 4-2 lead in the decider before Muguruza staged a comeback of her own to book her place in the second round against Daria Kasatkina.
Sixth seed Elina Svitolina eased into the second round with a 6-3 6-3 victory over Olympic champion Monica Puig.
"My game was quite solid. I didn't do so many unforced errors, which is good, because with couple of changes it can happen," the world number 14 said.
(Reporting by Amlan Chakraborty in New Delhi,; editing by Ed Osmond)
