James Beattie's side opened the scoring through Piero Mingoia on 20 minutes, before a mix-up at the back gifted David Dunn an equaliser just before the break.
Stanley regained the lead through James Gray 10 minutes into the second half, but more disastrous defending saw Tom Cairney presented with the simple task of securing a share of the spoils.
Gary Bowyer named a strong starting XI for the local derby at the Store First Stadium.
Paul Robinson, Markus Olsson, Corry Evans and Dunn were all handed their first run-outs of the summer, whilst new boy Alex Baptiste made his Rovers bow.
Regular centre-back pairing Grant Hanley and Matt Kilgallon lined up at the heart of the defence, the midfield quartet comprised of Josh King, Corry Evans, Craig Conway and Cairney, whilst star striker Jordan Rhodes spearheaded the Rovers attack.
A Rovers XI, including the likes of Simon Eastwood/Jake Kean, Adam Henley, Jason Lowe, Lee Williamson, Chris Taylor, Ben Marshall, Ruben Rochina and Leon Best lost 2-0 at home to Rochdale in a behind-closed-doors friendly earlier in the day.
Rovers made a bright start, with Dunn flashing a left-foot drive from the edge of the area just wide of the up-right inside two minutes.
There was then three chances in quick succession either side of the quarter-hour mark. First up, Baptiste failed to trouble the Stanley goal with an ambitious effort from the right flank.
A minute later, Hanley's ball over the top found Rhodes through on goal, but the Scot was uncharacteristically off target with his lobbed effort.
Straight up the other end, Josh Windass, son of ex-striker Dean, fired a crisp 20-yard strike just past Robinson's right-hand post.
However, the hosts did make the breakthrough with their next attack. Kal Naismith centred the ball from the right and Mingoia lashed a low shot into the bottom corner.
Stanley thought they'd added a second on 26 minutes when Gray headed home Windass' free-kick, but the number nine was flagged offside.
A minute later, King's goal-bound shot looked to strike an arm in the Stanley box, but Rovers' only reward was a corner.
Just past the half-hour, Stanley threatened again, with two efforts in quick succession. Gray's effort from the edge of the area was watched wide by Robinson, who then denied Mingoia with a smart save.
And the hosts were made to pay, as Rovers drew level just before the break. Kilgallon's cross caused confusion in the Stanley defence and Dunn was on hand to tap home the follow-up into the empty net.
Rovers made a double change at the interval, with Dunn and Olsson, who both linked up late for pre-season after only recently re-signing for the club, were replaced by Luke Varney and John O'Sullivan, but it was Stanley who looked the more dangerous.
Windass fired straight into the arms of Robinson, before the hosts regained the lead on 55 minutes when Gray raced onto Mingoia's through ball, before curling a superb first-time shot into the top corner.
However, for the second time in the game, calamitous defending gifted Rovers another equaliser. Goalkeeper Andrew Dawber tried to dribble the ball out from the back, Rhodes robbed him of possession, the ball broke kindly for Cairney, who rolled it into the open goal.
Rovers had a let-off on 71 minutes when Gray's left-foot shot bounced back off the far post and the hosts were unable to force home the rebound.
Conway fired a free-kick inches wide on 74 minutes, before Rovers' remaining starters were all replaced a minute later. Stanley also shuffled their pack.
Varney saw a left-foot shot find the side-netting 10 minutes from time, as Rovers pushed for a winner, but the game ended up all-square.
Next up for Rovers is Bradford City away this Saturday.
ROVERS: Robinson (Raya 75), Baptiste (Carson 75), Hanley (Lenihan 75), Kilgallon (Daly 75), Olsson (O'Sullivan 46), King (Mahoney 75), Evans (Jorge 75), Cairney (Tanner 75), Conway (Bauress 75), Dunn (Varney 46), Rhodes (Rittenberg 75).
ACCRINGTON: Dawber (Turner 63), Hunt, Liddle (Beverley 77), Joyce, Aldred (Atkinson 77), Winnard, Naismith (Clunan 76), Windass (Goulding 86), Gray (Ormerod 76), Hatfield (Martin 76), Mingoia.
Subs not used: McCartan, Jenkins.