Boxall's hopes of a medal were left hanging by a thread early in the competition when he failed with his first two attempts at the 152kg snatch, but he succeeded on his third and final try to remain in the competition.
Boxall - who finished fourth in Glasgow four years ago - was successful with all three of his efforts, including a best of 199kg to see him narrowly pip Osarfo to the podium by one kilogram.
Singh had his eyes on gold after succeeding with his first clean and jerk attempt of 200kg, but he failed with subsequent efforts at 209kg and 211kg.
Defending champion David Katoatau of Kiribati - who shot to fame with his dancing celebrations in Glasgow four years ago - only managed a fifth-placed finish this time around after only managing a 140kg snatch.
Boxall's medal - which comes on the final day of weightlifting action on the Gold Coast - is England's fifth of the Games, following on from one gold and three silvers.