The 24-year-old wildcard from Stockport, ranked 164, overcame the world number 94 2-6 7-6 (9-7) 6-0 to reach the second round.
But British number three Johanna Konta lost 6-4 3-6 6-4 to China's Peng Shuai.
James Ward, Dan Cox, Dan Evans and Kyle Edmund were also beaten in the men's singles first round.
Broady will face either 16th seed Caroline Wozniacki or Israel's Shahar Peer - Wozniacki led 6-3 2-0 when play was suspended for the day - in the second round.
Having lost her Lawn Tennis Association (LTA) funding as a 17-year-old in 2007 for "unprofessional behaviour" on a night out, Broady has had to pay her own way on the circuit since.
"I don't think they (the LTA) will try and take credit for it, I'll laugh in someone's face if they try and say it was them," said Broady.
"It's definitely made me hungrier. If I don't win, I don't have any money."
A year ago Broady was exploring alternative career possibilities, but she has guaranteed herself prize money of at least £43,000 with victory over Babos.
"When I was looking at other things to do, it was specifically because I couldn't fund my tennis," she recalled. "It was hindering my tennis and I wasn't getting the best out of it.
"This time last year I was lucky enough to get a wildcard into Wimbledon qualifying. The week before that, I was researching how to become an au pair, and going to go live in another country.
"I was going for Paris and looking at doing first aid courses, language courses, to become an au pair, because I couldn't afford to play tennis. But I won a qualifying round and that got me through for a while, then I had some wins in the doubles and that helped me pay for the singles."
Broady believes the fact she does not get LTA funding has made her hungrier for success.
"If I don't win, I don't have any money. I have to fight harder on court," she added.
"The difference a year can make is amazing. I think I'll be fine for a year or so now. It's very satisfying knowing that it's me that has achieved this."
Ward made 30 unforced errors, failed to convert any of his three break points and won just five games as he lost 6-2 6-2 6-1 to 17th seed Mikhail Youzhny, while Cox was beaten 6-2 7-6 (7-3) 6-7 (6-8) 6-3 by Frenchman Jeremy Chardy.
Evans was a 6-1 7-5 3-6 7-6 (7-5) loser at the hands of Russian Andrey Kuznetsov; while Edmund, last year's junior semi-finalist, found Austria's Andreas Haider-Maurer too strong and lost 6-3 7-6 (7-4) 6-2.
"It went OK," said Edmund. "I got off to a good start, but struggled a bit at the end of the first set. I'm glad I got my game back to take it to a tie-break. I thought I was unlucky to lose the second. He played a good third set. I have lots of experience to take, so it's not all bad."
Konta had lost in the opening round in both 2012 and 2013, but made a strong start in her encounter with Peng when she broke in the first game of the match.
However, the 23-year-old was let down by her serve and Peng broke twice to take the opener. Backed by the home support, Konta broke three times to take the second set, but Peng's consistency and well-placed serve proved too strong in the decider to seal victory.
"I believe I came back in the second set with a cool head and just started playing tennis," said Konta.  "In that third set, it was just one more break and she played a good service game to serve it out."
British number one Heather Watson, who reached the semi-finals in Eastbourne, begins her campaign against Ajla Tomljanovic on Tuesday, along with compatriots Daniel Smethurst, Samantha Murray and Tara Moore.
Earlier, Andy Murray opened the defence of his Wimbledon title with a straight-sets victory over David Goffin.
British number four Naomi Broady won her first match at a Grand Slam as she came from a set down to beat Hungary's Timea Babos at Wimbledon.