The 17-year-old fired the hosts into an early lead, but that was as good as it got for managerless Rovers against a far superior Sheffield side.
Sheffield started strongly, but Rovers' efforts were rewarded with a goal against the run of play on 10 minutes. Hardy, playing as the lone striker, received a ball to feet 20 yards out, before turning inside and firing a superb shot into the bottom corner.
From then on, it was one-way traffic towards the Rovers goal, as Sheffield scored three times in quick succession. Lisa Giampalma twice converted from corners, either side of a Zara Musker own goal. The visitors added a fourth goal through Krystle Johnston just before the break.
Having spent much of the first 45 minutes pinned back deep inside their own half, Rovers changed their shape and personnel after the interval, and it had the desired effect. Substitutes Amie Fleming and Hayley O'Donnell provided plenty of pace and energy down the flanks, which enabled Rovers to play further forward.
Sheffield had a golden opportunity to increase their lead following a foul in the box, but the penalty was superbly saved by goalkeeper Jo Hutcheson, who excelled throughout.
A fifth goal did arrive right at the death when Ellie Gilliatt's cross looped into the far corner, but interim manager Gemma Donnelly said that there were plenty of positives to take from Rovers' second-half performance going forward.
"I am immensely proud of the girls to keep the second-half scoreline goalless until the last 30 seconds," she said. "The character and attitude they showed was different class.
"After what had been a difficult few days, I have nothing but praise for the application and effort of the girls throughout.
"Everyone wants to compete and challenge for a better position in the league table, because the players feel that where we are doesn't reflect the potential of the team.
"They realise it's going to take time, but they are willing to put in the hard work to get to where they need to be."
ROVERS: Hutcheson, Middleton, Seed, McLellan, Musker, S. Hardy, H. Forster, Flynn, Marsh (Fleming 51), N. Forster (O'Donnell 51), R. Hardy.
Subs not used: Jackson, Noori.