Both boxers scored marginal wins, but impressed and were backed by a boisterous crowd who gave the two fighters their full support.
Bantamweight Campbell, who beat Italy's Jahyn Vittorio Parrinello 11-9, admitted the occasion got to him, but was pleased he did enough to get through his first Olympic bout.
"It wasn't my best performance but it was my first fight and my nerves were going," said the Hull-born fighter.
"I was trying to keep my cool and listen to the coaches and stick to the tactics. It is the biggest experience of my life. I have worked my life to get here.
"It is just about trying to keep calm but now I have got the first one out the way hopefully I will get better throughout the tournament.
"I always told myself I wasn't going to put pressure on myself and enjoy the occasion, but you can't get away from the pressure - it's there.
"It is the biggest event on the planet and it was my first fight. Have you seen the crowd out there? It would make anyone nervous."
Campbell, who couldn't believe he was fighting in front of boxing legends Lennox Lewis and Evander Holyfield, played down expectations of a being a medal winner, but says he's confident he can go all the way.
He said: "It's just people's opinions. At the end of the day it's me that has to do it - I have got to perform.
"I am confident. I have never worked so hard in my life to prepare for this tournament and I am confident in what I can do.
"I was told Lennox Lewis was here just as I was about to go out and I thought great but I didn't know Evander Holyfield was here. They are two legends of the sport."
Meanwhile, super heavyweight Joshua carried on Team GB's good form in the boxing when he defeated Cuba's Erislandy Savon Cotilla.
In a superb atmosphere at the ExCel, the London-born fighter made the perfect start by winning the first round by six points to five.
With Joshua throwing out some big jabs, he was caught on the rebound by Cotilla's counter-punches, but still managed to stay 14-12 ahead on the judge's scorecard.
But he was in trouble in the last round - losing by four points to three - but his hard work earned him the win and passage to the quarter-finals.