Baskerville took his goal tally for the season to 18 in Welfare’s first game for almost three weeks.
Jamie Austin also scored on his debut and Rhys Plater scored his second in Armthorpe colours.
Former Doncaster Rovers youngster Joe Pugh also made his debut for Lee Morris’s side, who moved up to 11th in the NCEL Division One table.
Welfare travel to Harrogate Railway Athletic on Saturday.
Rossington Main remain one place outside of the play-off positions in sixth after they were held to a 2-2 draw at Shirebrook Town.
Bradley Wells put Main ahead after 11 minutes but goals either side of the interval from Joshua Devereux and Kenan McKenzie turned the game on its head before Tyla Bell levelled from the penalty spot on the hour mark.
Rossington host Brigg Town in the third round of the League Cup on Tuesday night before welcoming Rainworth Miners Welfare to Oxford Street on Saturday.