Belgium were overwhelming favourites in their opening World Cup clash, but Roberto Martinezs men struggled to break down their Group G opposition before the break.
Lukaku had little impact in the opening 45 minutes but came to life following Dries Mertens opener just after half-time.
The Manchester United striker added Belgiums second with his head after Kevin De Bruynes pinpoint cross and completed his brace with a delicate dink in the 75th minute.
I told Romelu at half time that we needed him. He was hiding away on his own up front in the first half, Chelsea star Hazard revealed.
Even though we have good players, it is not easy for us to play with a man short.
Once he got involved in the game, as if by magic, he scored two goals. I hope he will understand.
He did not have a bad game. He scored twice, so everyone is happy. It is good for his confidence.
But I want him to try to get more involved in the game, especially during the first half – as we know what he can do.
Belgium boss Martinez believes his side controlled the game after Mertens spectacular opener.
That first goal was going to be essential, he said after the win.
It is almost a mental blow for one team and it gives you a lot of breathing space for your first game in the tournament, and I thought from that point on we were more ourselves, more in control.
It was our first World Cup game and we wanted it to be perfect.
We dont want to take any credit away from Panama. What they did in the first half, they deserve huge credit, and my players deserve credit for what they did in the second half.