England did not begin their U21 campaign as sharply as they would have liked.
England face hosts Poland in their final group game on Thursday, while Slovakia face Sweden.
But there was little serious threat from England despite plenty of possession - similar to the Sweden game - with only Chalobah's long-range effort dribbling wide.
England were back on level terms, though, just five minutes after the break as Mawson poked home from close range. A win will guarantee a place in the semi-finals, while a draw might be good enough depending on other results.
With only the top team in each group guaranteed qualification for the knockout stages, Aidy Boothroyd's team are available at 8/11 (1.73) with dabblebet to put themselves in pole position with a win in Kielce.
"It shows my players there's a pathway for them". "We've got to win and win the next one after that".
"Disappointed to concede from a set piece, considering how much we worked on them, but we will enjoy the moment".
The goalscorer Mawson is developing something of a reputation in front of goal having been one of only three centre-backs to find the net four or more times in the last Premier League season.
All things considered, odds of 17/20 (1.85) certainly look like a sensible investment on both teams finding the net for the sixth time in seven Slovakia matches, particularly given the urgency of England's situation.
He said: "I'm not satisfied because I want to win every game". Chelsea forward Tammy Abraham was involved in England's victor, holding the ball up to set the side on their way to a quick counter-attack, and his pace and strength are considerable assets. "He's been up there on his own and he has not got his goal over the two games but he doesn't half work hard for the side".
"It's really helpful having them here", Boothroyd said.
"Yeah I totally agree with Stuart, I thought he was brilliant", he said. He's a good player; he scores goals, he holds the ball up.