Rovers earned a well-deserved point at the Riverside as below-par Boro had to come from behind.
Paul Lambert’s deadline day signing Jordi Gomez put the visitors ahead in the second half but David Nugent salvaged it for Boro 11 minutes from time.
It ended back-to-back defeats for the promotion-chasing Teessiders as they went level with Hull at the top of the Sky Bet Championship.
Rhodes, signed from the Lancashire side on Monday, started on the bench for Boro as Aitor Karanka handed debuts to Ritchie de Laet and Kike Sola.
But it was the home side who started brighter, with Darragh Lenihan hitting an ambitious 25-yard effort after 15 minutes which Dimi Konstantopoulos did well to smother.
Rovers had the ball in the net moments later when Gomez’s curling free-kick was turned in by Elliott Ward but he was ruled offside.
And they wasted a great chance in the 20th minute, with Gomez at the centre of it again. His ball found Tony Watt inside the left side of six-yard box but he poked his shot inches wide of the far post.
The home side started to look the part after the half-hour mark and after some good build-up play involving Stewart Downing and Emilio Nsue, Grant Leadbitter saw a long-range shot flash wide of Jason Steele’s right-hand post.
Karanka made a change at half-time, with Christian Stuani replacing debutant Sola, who flattered to deceive on his Boro bow.
But it was Rovers who again looked the more threatening early into the second half as Tommy Spurr’s long throw-in caused problems in the Boro box. The loose ball fell to Lenihan but he shot wide.
Boro got going again after the hour. Albert Adomah forced a corner down the left and when Rovers struggled to clear, it fell to Ben Gibson but his snatched effort was well over.
Blackburn had a good opportunity to open the scoring when Nugent tripped Evans 25 yards out but Marshall’s free-kick sailed well over the crossbar.
Boro then had a glorious chance to break the deadlock in the 70th minute when Downing’s right-wing cross found sub Stuani in space but his header flew over Jason Steele’s bar.
Rovers grabbed the opener in the 72nd minute. Boro’s poor defending gifted Lenihan time to lay off for Gomez and the Spaniard drilled home a left-footed effort from the edge of the penalty area.
Rhodes was introduced to make his Boro debut in the 77th minute and the home side drew level two minutes later when Nsue’s right-wing cross was headed in at the far post by Nugent.
Rovers were close to edging in front in the 89th minute when Boro failed to clear Marshall’s free-kick and it fell to Hope Akpan inside the box but he dragged his shot wide.
Middlesbrough manager Aitor Karanka was unhappy with the display.
“The best example was the last 20 minutes because that was the only time we wanted to win the game,” he said.
“The first 70 minutes we haven’t played with the intensity that we need to play, especially after our last two defeats.
“I thought the reaction today was going to be better, but the last 20 minutes is the only time we wanted to win or draw the game when we had a few chances.
“I know the concern, now we try to motivate them as we were two or three weeks ago. So now we try to work more and try to pick the right players.
“The problem is the goalkeeper was completely lost because five or six players around him did nothing.
“It’s a difficult league, and when your team-mates do nothing it’s difficult to perform.”