In a game dominated by the hosts, Graham nodded in Liam Feeney's cross to put Rovers ahead on 81 minutes
But, after several near misses, Wells got it right in the 94th minute.
From a right-foot free-kick just outside the box, he bent his sixth goal of the season into the top left corner.
Although denied a first win since 26 November, Owen Coyle's Rovers did at least end the run of four straight defeats they had suffered since drawing 1-1 with Huddersfield at Ewood Park on 3 December.
They remain 22nd, two points adrift of safety, while Huddersfield edge a place up above West Yorkshire rivals Leeds United back into fourth.
The Terriers' run of four straight victories since the first Blackburn game came to an end, but they had enough chances to have maintained their winning run.
In the first minute, Rovers keeper Jason Steele made a double save from Rajiv van La Parra's volley and Kasey Palmer's bicycle kick from the rebound.
Eight shots rained in on the Blackburn goal inside the first half hour, while Wells twice shot over, But, although it looked like a classic hit and run when Rovers went ahead, David Wagner's men held their nerve,
Huddersfield head coach David Wagner: "Nahki is a natural goalscorer and if he stays in the game and works hard then we stay in the game."
"If the opposite of disappointed is happy, then I am happy with the result.
"Few teams would have come back after playing as well as we did and then conceding a late goal. For that reason I am happy.
"The players still trusted and believed in themselves and they kept going right to the end."
Blackburn boss Owen Coyle: "You have to say it was a fantastic point for us against a team that's going well, who I expect to be in the top six at the end of the season.
"But we had given ourselves a great position to win the game and from that point of view it's hard to take.
"We were very disciplined and kept our shape. They had a couple of wonderful chances in the first half and Jason Steele made a couple of good saves, but they had little in the second half.
"We have proved we are capable of scoring goals but we must now start keeping clean sheets and when we are in a good position we must do what it takes to get over the line."
Match ends, Huddersfield Town 1, Blackburn Rovers 1.
Second Half ends, Huddersfield Town 1, Blackburn Rovers 1.
Mark Hudson (Huddersfield Town) wins a free kick in the attacking half.
Foul by Wes Brown (Blackburn Rovers).
Goal!  Huddersfield Town 1, Blackburn Rovers 1. Nahki Wells (Huddersfield Town) from a free kick with a right footed shot to the top left corner.
Jack Payne (Huddersfield Town) wins a free kick in the attacking half.
Foul by Elliott Bennett (Blackburn Rovers).
Offside, Blackburn Rovers. Liam Feeney tries a through ball, but Sam Gallagher is caught offside.
Offside, Blackburn Rovers. Elliott Bennett tries a through ball, but Sam Gallagher is caught offside.
Foul by Chris Löwe (Huddersfield Town).
Sam Gallagher (Blackburn Rovers) wins a free kick on the right wing.
Substitution, Blackburn Rovers. Wes Brown replaces Danny Graham.
Attempt missed. Hope Akpan (Blackburn Rovers) right footed shot from outside the box is high and wide to the right following a set piece situation.
Foul by Mark Hudson (Huddersfield Town).
Gordon Greer (Blackburn Rovers) wins a free kick in the defensive half.
Attempt missed. Michael Hefele (Huddersfield Town) right footed shot from the right side of the six yard box misses to the right. Assisted by Aaron Mooy with a cross following a corner.
Substitution, Huddersfield Town. Mark Hudson replaces Dean Whitehead.
Corner,  Huddersfield Town. Conceded by Ryan Nyambe.
Attempt blocked. Jack Payne (Huddersfield Town) left footed shot from the centre of the box is blocked.
Attempt blocked. Chris Löwe (Huddersfield Town) right footed shot from the centre of the box is blocked.
Attempt missed. Tommy Smith (Huddersfield Town) right footed shot from outside the box misses to the left following a corner.
Corner,  Huddersfield Town. Conceded by Jason Steele.
Attempt saved. Jack Payne (Huddersfield Town) left footed shot from the left side of the box is saved in the top left corner. Assisted by Chris Löwe.
Goal!  Huddersfield Town 0, Blackburn Rovers 1. Danny Graham (Blackburn Rovers) header from very close range to the bottom right corner. Assisted by Liam Feeney with a cross following a set piece situation.
Foul by Elias Kachunga (Huddersfield Town).
Hope Akpan (Blackburn Rovers) wins a free kick on the left wing.
Christopher Schindler (Huddersfield Town) wins a free kick on the left wing.
Foul by Sam Gallagher (Blackburn Rovers).
Jack Payne (Huddersfield Town) wins a free kick in the attacking half.
Foul by Hope Akpan (Blackburn Rovers).
Attempt blocked. Harry Bunn (Huddersfield Town) right footed shot from the left side of the box is blocked. Assisted by Jack Payne.
Foul by Aaron Mooy (Huddersfield Town).
Ryan Nyambe (Blackburn Rovers) wins a free kick in the defensive half.
Offside, Blackburn Rovers. Gordon Greer tries a through ball, but Sam Gallagher is caught offside.
Substitution, Blackburn Rovers. Elliott Bennett replaces Corry Evans because of an injury.
Delay over. They are ready to continue.
Delay in match Corry Evans (Blackburn Rovers) because of an injury.
Attempt missed. Tommy Smith (Huddersfield Town) left footed shot from the right side of the box misses to the left. Assisted by Nahki Wells.
Attempt blocked. Harry Bunn (Huddersfield Town) left footed shot from the centre of the box is blocked. Assisted by Elias Kachunga.
Foul by Harry Bunn (Huddersfield Town).
Huddersfield Town striker Nahki Wells rescued his side with an injury-time equaliser as Championship strugglers Blackburn Rovers were denied the chance to climb out of the bottom three.