Jones said: " I don't blame other people's actions. I still should have scored."
After a Pittsburgh punt, Flacco escaped pressure to complete a 34-yard pass to Jones, and Tucker put the Ravens up by 12 with 13:59 remaining.
That would be Baltimore's final score, and it proved to be just enough for a much-needed victory.
Baltimore limited the Steelers to 98 yards in taking a 10-0 halftime lead.
Baltimore moved 71 yards on its first drive to take a 7-0 lead on a 7-yard touchdown pass to Smith. The play came after Smith hauled in a 54-yard pass from Flacco to the Pittsburgh 1.
There were three scuffles after the whistle in the first quarter, but peace was restored before things got out of hand.
Pittsburgh's third drive ended with a curious, aborted field-goal try. Shaun Suisham was poised to kick a 50-yarder, but his approach began well before the snap and he didn't follow through. Holder Mat McBriar flipped an impromptu lateral to Suisham, who was tackled for a 12-yard loss.
" Our timing was really off," Suisham said.
The Ravens then took advantage of a 26-yard pass interference call against Ike Taylor to go up 10-0.
Notes: The Steelers reported several injuries, including Bell (concussion), DE Brett Keisel (foot), G Kelvin Beachum (knee), OT Mike Adams (ankle), G David DeCastro (foot), OL Fernando Velasco (ankle). ... Baltimore's streak of sacks in 22 straight games ended.