The 27-year-old striker has struggled since his free transfer from Leeds last summer but was on target in Saturday's convincing 5-1 win at Scunthorpe in the FA Cup third round. It was his fourth goal of the season and came against a club that helped establish him in professional football.
Round said: "Jermaine is really finding his feet in the Premier League. He scored again and that was very pleasing. We know he can score goals, he is a really good finisher. He has now got a goal, he was threatening the other night and we are really pleased with his progress."
Beckford grabbed Everton's second goal after Louis Saha had got the Toffees off to a fine start at Glanford Park with a fourth-minute strike.
Michael Collins pulled one back against the run of play as Scunthorpe briefly threatened a fightback but goals from Seamus Coleman, Marouane Fellaini and Leighton Baines killed them off.
Beckford, making a second successive start after featuring against Tottenham in midweek, was a threat throughout and Scunthorpe manager Ian Baraclough was also impressed.
Baraclough, who played alongside Beckford for the Iron, said: "He looked bright and didn't look out of place in their team. I just hope he can prove himself to be a good striker at that level, because he is a good striker.
"It is all about confidence. Jermaine could have gone in there thinking it is all too much for him but it certainly isn't. I'm pleased for him. I'm disappointed he scored, obviously, but he is a good kid and deserves success."
Everton can now look forward with confidence to next week's Merseyside derby against Liverpool after following up their confidence-boosting win over Spurs in impressive fashion.
Round said: "We are very pleased. I think we have been threatening that sort of a result for a while. It is just pleasing to get the goals and go through to the next round. It is very important to score early because the opposition can get up a head of steam if the crowd gets behind them."
Source: PA
Source: PA