The Brit collided with Kevin Magnussen on the opening lap of the race, but went on to seal a top-five finish following an incredible display in Barcelona.
Hamilton finds himself 64 points behind championship leader Max Verstappen, but with over 400 points still up for grabs, Mercedes boss Toto Wolff is confident his driver can get back into the world title hunt.
He said: "That looked like a world championship-winning race car that Lewis was driving.
"His race pace was stunning and [without the first-lap incident] he would have challenged for the win.
"It reminded me of last year and the years before, when a car and driver are really on the top of their game. The race was so important for his morale and our morale, too.
"The car was like previous seasons, where you are more than 30 seconds behind the whole field, and you come all the way to the front and near the podium. That is very encouraging and shows that we've made another step."
The 50-year-old Austrian apologised to Hamilton four weeks ago as the Brit finished 13th at Imola in an 'undriveable' car.
However, the team's first major upgrade since the start of the 22-race season appears to have rescued the bleak situation.
Wolff added: "It is better than I expected because I am pessimistic. But we have pulled clear from the midfield, and we have caught up by half-a-second to the frontrunners, when we were a second off in Miami. There is more to come and more understanding which we can unlock in the car.
"We have two unbelievable drivers and the right guys to sort our car out and bring us back to the front."