Cousins overhauled three-time world medallist and single sculls specialist Campbell in the final 250 metres - and admitted he was shocked by the win.
"Let's not get carried away, it's only one race but I'm really happy with the win, although it's a bit of a surprise really," he said.
Helen Glover, the Olympic women's pairs champion, won the women's singles sculls, holding off a determined challenge from two-time Olympic quadruple sculls silver medallist Frances Houghton.
"In that final 100m I just shut my eyes and went for it as I knew that Fran has a good sprint finish," said Glover, whose margin of victory was the narrowest of the day.
Elsewhere, Andrew Triggs Hodge, Olympic men's four champion, and Moe Sbihi from last year's Olympic bronze medal eight, were emphatic winners of the men's pair ahead of their rivals and also Olympic men's four champions Peter Reed and Alex Gregory.
"We knew in training that everything was going pretty well but you still have to do it on the day," said Hodge.
"What Moe did was superb and we worked really well together."
Elsewhere, Imogen Walsh and Peter Chambers won the lightweight single sculls events, giving British team officials plenty of food for thought ahead of the forthcoming World Cup regattas and this year's World Championships.
"We have had some great racing today and it is very healthy to see some new blood challenging for top places in the finals," said Sir David Tanner, GB Rowing's performance director.
"We have Rio in our sights but this season will be important to lay down a base for the next three years as well as some experimentation with new boat mixes.
"Over the next few weeks we will be forming our boats for the next World Cup on home waters in late June at Dorney."