Having crashed at home defeat against Lobi Stars, a solitary effort from Ajibola Otegbeye was all the Owena Whales required to secure winning ways return.
And the former Gombe United gaffer admitted his side dig deep to see off the strong People's Elephants in front of an empty Akure Township Stadium.
"It was a hard-earned victory by the boys against an almighty Enyimba," Eguavoen told Goal.
"It came as a huge relief for us. The game was not smooth for either side. I expected Enyimba to do a lot better than they did.
"We could see that Enyimba has a lot of experience players. If we go down the memory lane, they have a great history.
"For my boys to come out with a 1-0 victory over Enyimba is not a bad idea at all.
"Despite my boys were playing under intense pressure and for them to hold their nerves and come out to play like this. I'm quite pleased," he concluded.