The Eagles got the win that mathematically secured their top-flight status as they overcame the already-relegated Blades at Bramall Lane on Saturday.
Christian Benteke's early goal and Eze's late clincher ensured Hodgson's side won 2-0 to end a three-match losing run.
Eze, signed from QPR last summer, was a menace throughout with his driving runs and capped a fine performance with a goal two minutes from time.
Another wonderful solo dart, similar to that which created Benteke's goal, saw the winger slip away from John Lundstram midway inside his own half by the touchline and head for the penalty area. He had options to set up a team-mate but decided to shoot, with his effort striking John Fleck and wrong-footing Aaron Ramsdale
"He was very good, wasn't he?" said Hodgson. "It was a bit of a baptism of fire with three games in a row against Chelsea, Leicester and Manchester City, in that it's not easy against the likes of those teams to get on the ball and show your silky skills.
"But we know that's the quality he possesses and we encourage it. We constantly say to him and back him and won't criticise him if he tries something and it doesn't come off.
"He was bold with the ball today and drove forward at every opportunity. He wasn't looking to release it too soon, and he got his reward right at the end with the goal.
"If you ask me if I'm happy with Eberechi Eze, I say absolutely. It is his first season coming up from the Championship and you expect people to need time to adjust and play at this level."
Palace were all but safe from relegation before arriving in Sheffield but victory at Bramall Lane made absolutely sure – not that Hodgson was ever concerned.
"I'd not really worried about it, to be honest. Even though we have been stuck on 38 points for a few weeks, it never occurred to me that we were in a relegation scrap," said Hodgson.
"I'm delighted with the win today and it gets us over the 40-point mark as well."
Another impressive performance from Ramsdale was the only positive for the Blades.
The England Under-21 goalkeeper made a couple of fine saves to keep his team in the game at 1-0 and the goals he did concede both took huge deflections, giving him no chance.
Interim boss Paul Heckingbottom said: "I've spoken all along about how impressed I've been with him. Before, I was watching from a distance and not working with him, and he has impressed me massively.
"He's come through a difficult spell at the start of the season and that shows his character.
"He made a great save from Benteke but he also showed that he is good with his feet and it was a strong performance from him."
On the game itself, Heckingbottom added: "Conceding in the first 90 seconds or whatever it was just set the game up for them, it knocked the stuffing out of us.
"How Palace play and how good they are on the counter-attack, it just set it up for them and made it difficult for us to get any sort of foothold in the game. It took an awful long time to try to wrestle that back."