As Henry's free throw swished through the net on the front end of a one-and-one, Richmond's Derrick Williams and the 49ers' Willie Clayton became entangled setting up for a potential rebound.
Back came the hosts and they came close to an equaliser soon after the interval as Samba nodded on a long throw and would have found the net had it not been for the well-positioned substitute Yuri Zhirkov, who cleared the danger from the line.
Hamilton were in front nine minutes before half-time when Falkirk failed to clear Easton's throw-in and the ball fell to McCarthy, who lashed into the net past Flinders.
And things got worse as keeper Iker Casillas failed to handle a long throw just before halftime and Pablo Garcia lobbed the loose ball over him into the net.
Soon afterwards, Givet gave Rovers the lead with a stunning strike - smashing the ball into the corner of the net after Ciaran Clark had half-cleared Morten Gamst Pedersen's throw.