Hulkenberg, who has not raced at Barcelona since 2019 with Renault, ended the second practice session on Friday afternoon behind only Fernando Alonso and Red Bull pacesetter Max Verstappen.
The German, who was yet to take the 170mph final corner flat out, eventually posted a 1m14.177s as he ran 0.27s off the pace. A margin of 0.536s covered the following 12 cars down to his team-mate Kevin Magnussen in 15th.
Hulkenberg, who had only classified 18th in FP1, reckoned his performance had been "genuine" at the time of FP2, although expected other teams to find pace heading into Saturday running.
He, therefore, called on his team to "stay cool and realistic" despite the heady result.
Hulkenberg said: "I think it looked genuine, but I guess other people kind of underperformed, underdelivered.
"Especially, there's a lot of top cars that I think they will find something overnight or pick it up. We've got to stay cool and realistic."
Hulkenberg, who has yet to score a podium in F1, reckoned the Haas was far better suited to the permanent Barcelona track after he ran to only 17th last time out in Monaco (hurt by a 10s penalty for an incorrectly served pitstop), despite the car sporting an upgraded front wing in the principality.
He continued: "For me, it's important to have a good feeling in the car, a good rhythm.
"I managed to find that today, which is the most important thing for me and for a driver.
"Obviously, I'm hoping to have a similarly good day tomorrow. Just squeeze out what we have.
"But it is going to be tight again. Even the Q3 fight, if you see in the midfield, there are still four or five teams and we're all battling for the same piece of Tarmac.
"It's going to be a tough, tight fight again… Naturally also here, the car is just in a much happier place. It immediately gives me a better feeling compared to a week ago in Monaco."
He added: "It felt decent, especially that lap. New softs give you a lot of grip over one lap.
"Particularly for FP2, I think we've picked up some performance. In FP1, it wasn't quite there yet."
Meanwhile, Magnussen, seventh in FP1, reckoned set-up tweaks for the later session had hurt his speed.
