The visitors were playing much the better football, and a precise passing move saw Stephen Warnock force a decent save from Jones before Benni McCarthy put a curling effort well wide.
Grella was the next to try his luck with a well-executed volley from the edge of the box and Santa Cruz forced Jones into an improvised save with his legs.
Santa Cruz was controversially penalised for handball after getting on the end of a Tugay pass, although his method of control looked at least as legal as the one he employed to score against Bolton midweek.
The second half was a similarly hard-fought affair, with an early chance for Boro midfielder Josh Walker denied by Pedersen's tackle.
Allardyce rues Blackburn wastefulness
A nasty clash of heads between Samba and Tuncay stopped play for several minutes, but the blood-splattered Boro striker played on after receiving treatment.
Jones tipped over a long-range effort from Tugay before Boro substitute Afonso Alves added some spark with a dangerous run and low shot that Paul Robinson saved well.
Blackburn were still the more dangerous side though, and Boro were grateful to survive two goalmouth scrambles with McCarthy and Santa Cruz both finding their way blocked by desperate defending, while David Dunn also had two decent efforts saved.
And Jones made himself the hero for Boro late on with two fine saves from Roberts, the first from an acute angle, the second from a header inside the six-yard box.
Middlesbrough boss Gareth Southgate:
"A point is probably fair. It was a tense afternoon and a scrappy game.
"We knew we'd have to defend strongly and we did. But Brad Jones made some fantastic saves and everybody worked hard for us.
"In the long run that could prove to be a very important point for us."
Blackburn boss Sam Allardyce:
"We produced several opportunities and we should have won the game and this is happening too often when chances are going begging.
"We are not burying the opposition when we are on top and as a result we have found ourselves in the bottom six.
"I'm pleased that we have kept out unbeaten run going but we should have far more wins in this period."
Middlesbrough: Jones, Wheater, Riggott, Huth, Pogatetz, Adam Johnson, Bates, Walker, Downing, King (Emnes 65), Sanli (Alves 65).
Subs Not Used: Turnbull, Hoyte, Shawky, Arca, McMahon.
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