Resuming 8-1 clear overnight, Bingham knocked in a break of 73 to move 9-1 clear.
Baird responded with 46 to win his second frame of the contest, but Bingham finished matters off with a 79.
"Thankfully for me I got on top of Sam pretty early and he started feeling the nerves of playing his debut here," said Bingham. "I was 8-1 down to (Stephen) Hendry at the end of the first session last year so I know exactly how it feels, and it was important for me to get the job done as soon as I could tonight.
"I have always had the self belief and in the last two years I have actually proved it. There are loads of tournaments so you have so many chances to do well. This is my 29th tournament this season, who would have thought that a few years ago?
"I was practising with Mark Davis just before he came up here so I knew he was in good form. Back home he beat me 10-9, on my table. It is going to be a tough game."
Bingham begins his match against Davis in the last 16 on Sunday morning at 10am (BST).
FIRST SESSION REPORT
Stuart Bingham produced a masterclass against World Championship debutant Sam Baird to take a 8-1 lead into Thursday's deciding session.
Bingham settled immediately against his inexperienced opponent, producing a break of 64 on his way to the opening frame and quickly added a second, capitalising on Baird’s tentative play to display his brilliant natural potting ability.
Bingham was not playing flawless snooker, but he was n’o being made to pay for his mistakes by his anxious opponent, and Bingham quickly raced into a 4-0 lead at the mid-session interval.
Baird, who turned professional in 2009, had no answer as Bingham raced into a 6-0 lead, but he took heart as the Sheffield crowd got behind him and urged him to get on the board. A cagey seventh frame ensued, but Baird held firm and finally demonstrated his raw ability with a sweeping break of 87, the highest of the match, to close the gap to 6-1.
A renewed Baird looked to build on that in the next frame, but he failed to take his chances again, missing a red to the right middle and allowing Bingham to clean up to make it 7-1.
Baird’s hopes of giving himself a fighting chance had long since been extinguished, but his night got worse in the final frame when Bingham recorded a silky break of 80 to put him firmly in the driving seat.
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