When Rovers defender Dennis Souza received his second yellow card in the 58th minute, the stage was set for United to emerge victorious on Adams' home bow at Bramall Lane.
Yet Billy Sharp, a lifelong Blades fan who failed to sparkle during his time at the club, opened the scoring in the 66th minute and added a second from the penalty spot eight minutes later to put Doncaster 2-0 up.
United were on course for a fourth straight defeat but substitute Daniel Bogdanovic scored in the 86th minute and Rob Kozluk rifled home in the sixth minute of stoppage time to cap a spirited fightback.
Adams, who last week was handed a two-and-a-half year deal as successor to Gary Speed, said: "I am absolutely delighted. It was a cracking game and we showed a lot of character, especially when we were 2-0 down. To get a point, we will accept that and move on.
"That spirit is what this club is all about and I can remember when Neil Warnock was here. It was amazing how many times they scored in the 90th minute and it showed the character in the side."