The City Ground was vital in earning Forest most of the points that led them to safety last season. Forest have now equalled their Premier League club record of four successive home victories. The last occasion was in January 1996.
The lead was taken inside the opening three minutes when Brennan Johnson teed up Serge Aurier on the right and the defender sent in a perfect cross for Awoniyi to power home a header from six yards.
Sheffield started the second half on the front foot and were level in the 48th minute after debutant Hamer introduced himself in style following his arrival last week. Forest could not clear a corner properly and it fell to Hamer 20 metres out. He sent a curling effort into the top corner to send the visiting fans wild.
The Blades were rampant and Forest had to weather the storm, but they still carried a threat on the break, with the pace of Awoniyi causing problems.
Forest got their reward late on when Wood, who went on for Awoniyi, headed home another pinpoint Aurier cross from the right.
Wood’s 56th Premier League goal tied him with Tim Cahill on third-most for players from Oceania. Mark Viduka leads with 92, then Harry Kewell with 57.