The draw for Wednesday preserved manager Dave Jones' unbeaten record.
Nathan Tyson and Jake Buxton had put Derby 2-0 up before Chris O'Grady's long-range stunner got the Owls back into it before half-time.
Wednesday dominated the second half but looked to have been frustrated before Johnson's 90th-minute header handed them a point and ensured that Jones has still to taste defeat while in their dugout.
Jamie Ward returned from international duty for the Rams to replace Theo Robinson while academy product Will Hughes was also drafted in and Paul Coutts and Richard Keogh made league debuts.
The visitors brought Rhys McCabe into the side for his debut while Necj Pecnik, making his first league appearance, moved up front to make space in midfield.
O'Grady came in alongside Pecnik while Chris Kirkland and Anthony Gardner made their first league starts.
The home side opened the scoring after 11 minutes. Ward broke down the left and supplied a cross for the unmarked Tyson to slot past Kirkland and score his first league goal for the club after an injury ravaged 2011/12 season.
Summer-signing Coutts was looking lively for the Rams and his industrious work produced a result as centre-half Buxton, who scored twice in midweek against Scunthorpe, stooped low to head home a cross and double the lead in the 27th minute.
Four minutes later it was only Kirkland who stopped it becoming 3-0 as Tyson's snapshot in the area was impressively saved by the former England goalkeeper.
Derby were good value for their lead but Wednesday got one back against the run of play in the 39th minute as O'Grady gathered the ball on the edge of the area and hit an unstoppable shot into the top corner to reduce the arrears at the break.
Kirkland was Wednesday's hero again in the 49th minute as Ward hit a free-kick from 25 yards which took a deflection but the keeper did well to save low to his left.
Striker Gary Madine then replaced Pecnik but it was Jermaine Johnson who created the next opening as he went on a run but could only blast his shot over the bar.
O'Grady was on the hunt for a second screamer and took a shot from the edge of the box, but this time Frank Fielding was able to tip his shot over.
Buxton then went in the book for time wasting before Madine found the back of the net but his effort was ruled out for offside.
Wednesday had the ball in the net again in the closing stages but play had already been brought back for handball as the Owls were frustrated.
But their frustration turned to joy as Madine knocked the ball down and Johnson was on hand to head home.