The England manager saw his bold move to select 22-year-old Tottenham winger Andros Townsend for his debut pay off spectacularly when he scored a stunning goal and picked up the man-of-the-match award in Friday's 4-1 win against Montenegro.
He now believes England, who top Group H after an unbeaten campaign so far, will book their flights to Brazil next summer, although he has warned his men against complacency.
Hodgson said: "The job's half done. If we want to qualify direct we need to win against Poland on Tuesday night. That won't be easy. That will be very difficult.
"If they play as well against us on Tuesday as they did against Ukraine it will be a tough game."
Ukraine beat Poland to stay one point behind England and have a footballing 'gimme' with their last fixture against San Marino.
Hodgson, however, said: "I always back the players. I trust them. We are still unbeaten in this qualifying group. We are capable of going unbeaten in the 10th one and with the backing we got from the fans and playing at Wembley I have got to back them. I would be foolish not to."
Wayne Rooney scored the opening goal against Montenegro at Wembley, which was swiftly followed by a bizarre own goal from Branko Boskovic.
Dejan Damjanovic pulled one back for Montenegro but 22-year-old Townsend's strike and a late penalty from Daniel Sturridge after he was brought down in the area clinched the victory.
Hodgson admitted the selection of Townsend was a tough decision but said: "He made a big impact. He got the man of the match which he must be delighted with. It can't be easy for a young man making his debut in a game of that nature.
"He deserves all the credit which I am sure he is going to get because he played well, with a calmness and composure which I have seen him play with for QPR and most recently Tottenham. I was fortunate he was able to reproduce it.
"We had a lot of time to think about our selection. It was not easy to leave people like James Milner and Jack Wilshere out, as they also bring a lot of attacking flair.
"We thought Townsend's pace against a packed defence would open doors. He really performed on the night."