Chris O'Grady struck a goal in each half to secure three points for the Reds in an entertaining match at Oakwell.
Steven Davies nodded a header towards goal but Steele held well on five minutes, and as the Reds countered, Osbourne was booked for a cynical hack on Jennings.
At the other end Brek Shea's deflected effort left Gilks as an admirer but the shot went just wide of the near post. O'Grady then nearly nicked the ball from the Blackpool 'keeper moments later when Shea's cross wasn't cleared.
On 20 minutes Ramage's header cleared the far post and O'Grady crossed in the rebound for O'Brien audacious flick but his attempt at Gilks - who knew nothing about it, and gathered O'Brien's rebound - it would have been an incredible goal had the Scot's first attempt gone in.
A threaded pass from Jacob Mellis on 34 minutes had slightly too much on it for O'Grady to go one-on-one as the Reds raced down the middle.
Although both 'keepers weren't in too much action, the game was stretched as both sides had a clear intent to attack.
Just as the half time whistle was to be blown, Dawson found himself in on goal and was set to go round Gilks only to be brought down. Chris O'Grady stepped up to smash into the top corner and give his side the lead.
Two minutes after the break Ryan McLaughlin - who was having a fine debut - stood a lovely cross up but nobody was on hand to nod home. Thankfully, not too long later Jim O'Brien brought down an awkward ball from the sky and crossed for O'Grady who powered his header into far corner for 2-0.
Blackpool made two changes as Nathan Tyson and Michael Chopra replaced Martinez and Osbourne.
The Reds were pressing for a third and executing some nice passes down the left with O'Grady holding the ball up well and bringing team-mates into play.
A free-kick was curled wide from 22 yards by Jacob Mellis after O'Brien was brought down.
Steele did well to claw away a deep free-kick from the visitors on 73 minutes as Paul Ince's side looked for a way back into the tie.
O'Grady was running the show up top for the Reds as Blackpool simply couldn't get the ball off the big man.
The Reds made their first change as Brek Shea was replaced by Reuben Noble-Lazarus on 78 minutes.
Jacob Mellis made way for Liam Lawrence to make his Oakwell debut with seven minutes of normal time remaining.
On 86 minutes Paul Digby came on for Chris O'Grady - who appeared to be suffering from a dead leg.
Four minutes of added time was indicated by the Fourth Official but the Reds kept their clean sheet and bagged all three points.
Reds: Steele, Kennedy, Ramage, Cranie, Dawson, Mellis (Lawrence 83), McLaughlin, Jennings, O'Brien, Shea (Noble-Lazarus 78), O'Grady (Digby 87).
Subs: Dibble, Nyatanga, McCourt.
Blackpool: Gilks, Robinson, Broadfoot, Cathcart, Basham, Bishop (Harris 80_, Ferguson (c), Ince, Angel (Chopra 49), Osbourne (Tyson 53), Davies.
Subs: Warner, Eccleston, Caton, Cameron.
Attendance: 9866 (536 away)
Man of the match (sponsored by Napoleon's): Jim O'Brien