The Manchester United forward headed home Mexico's last goal in a 3-1 win over Group A rivals Croatia on Monday as Miguel Herrera's men ensured progression to the next stage.
Captain Rafael Marquez and winger Andres Guardado were also on the scoresheet for Mexico in a dominant performance.
Croatia were reduced to 10 men late on as Ante Rebic was sent off for a rash challenge on Carlos Pena.
Mexico will now face the Netherlands in the second round and Hernandez knows that staying calm will be key to their hopes of reaching the last eight for the first time on foreign soil.
"We're really happy, really pleased," Hernandez told FIFA.com.
"We have to stay very calm, very humble and not get carried away. This is just one more step forward, a very important one, but just one more step.
"If we want to make history we have to beat the Netherlands and keep moving along the path we've set out for ourselves."
Hernandez's effort was his first for his country in 13 matches.
And, after a difficult domestic season at Old Trafford, the 26-year-old was delighted to bring that drought to an end.
"This whole year has been very tough," he added.
"Players need confidence more than anything else, and I've been very short of it. Very few people have shown faith in me over this past year."
Mexico face the Netherlands in Fortaleza on June 29.
