The Scotland striker, who netted 25 times for Rovers last season, bagged a late leveller from the penalty spot after Daniel Nardiello had headed the home side in front.
On a busy night for the officials, both sides had goals ruled out for offside in a first half that Rovers dominated for long spells.
The turning point in the game arrived on the stroke of half-time, as Lee Williamson saw red for an over-the-ball tackle on Ryan Lowe.
Bury looked to have won it when Nardiello headed home Chris Hussey's free-kick on 71 minutes, but with just five minutes remaining, Josh King was brought down in the box and Rhodes made no mistake from 12 yards.
Rovers boss Gary Bowyer was once again hampered by illness and injury concerns ahead the game, with Rudy Gestede (ill), Chris Brown (knee), Ben Marshall (ill), Matt Kilgallon (back), Chris Taylor (dead leg) and Alex Baptiste (foot) all missing.
Jason Lowe started at right-back, youngster Jack O'Connell partnered captain Grant Hanley at the heart of the defence, whilst King provided support for Rhodes in attack.
A Rovers XI including Adam Henley, Marcus Olsson, Ruben Rochina, David Dunn and Luke Varney played in a behind-closed-doors friendly at Brockhall earlier in the today.
Rovers made an electrifying start, with Craig Conway posing plenty of problems for the League Two side early on.
On three minutes, his superb solo run down the left earned Rovers a corner amidst half-hearted appeals for a penalty.
A minute later, Corry Evans let fly from 25 yards, forcing Bury keeper Shwan Jalal into a fine diving save.
On six minutes, another Conway corner was flicked on by Hanley and headed goalwards by O'Connell, but Jalal made a comfortable save.
Rovers then twice went close in quick succession. After Conway again did well down the left, Evans played a neat one-two with Rhodes, but skewed his shot well wide. Seconds later, King burst into the box down the right, centred for the fast-arriving Williamson, who just couldn't take the ball in his stride.
Bury's first chance of the game arrived on 19 minutes when Williamson gave away a free-kick in a dangerous position, but Hussey's left-foot effort was watched wide.
Rovers were denied the opening goal on 25 minutes when King's shot on the turn deflected in off Rhodes, but the striker had just strayed offside.
Nardiello's stunning 30-yard drive flew inches over the bar moments later, before Bury too had a goal disallowed. Danny Mayor made a superb break through the centre, before playing the ball out wide to Chris Sedgwick and his cross was swept home by Ryan Lowe, who was also flagged offside.
Rovers responded well, with Conway's attempted curler from the edge of the area tipped away by Jalal, before Jason Lowe blazed over the bar.
But the half ended on a sour note for Rovers, as Williamson was shown a straight red card for a poor challenge on Ryan Lowe.
Bowyer, who watched much of the second half from the stands, was forced to reshuffle his pack at the break, with right-back Anthony O'Connor coming on for Evans, meaning Jason Lowe moved into midfield.
The Rovers substitute almost made an immediate impact, breaking down the right, before cutting inside onto left foot and seeing his crisp strike well saved by Jalal at his near post.
Conway then had two chances in quick succession - firing inches over from distance with a well-struck shot, before stroking King's cut-back just past the post - as Rovers made a bright start to the second half.
Bury came back at Rovers, with Ryan Lowe's attempted curler comfortably saved by Robinson on 65 minutes, before Craig Jones delivered a deep cross from the right, which Nardiello headed over at the back post.
The former Manchester United man made no mistake moments later however. O'Connor was guilty of giving away a free-kick, Hussey whipped it in from the right and Nardiello headed home at the near post.
Rovers responded well, with Conway curling a free-kick inches wide, before Nicky Adams went equally close at the other end.
With time running out, Rovers' spirit shone through and they grabbed the equalising goal their determined attacking approach duly deserved. Sandwiched between two defenders, King was felled in the box and Rhodes sent keeper Jalal the wrong way to preserve Rovers' unbeaten pre-season record.
Next up for Rovers is Stoke City at Ewood Park this Sunday.
BURY: Jalal, Jones, McNulty, Adams, Mayor (Trialist 83), Hussey (O'Brien 74), Sedgwick (Etuhu 46), Lowe, Nardiello (Thompson 77), Soares, Mills.
Subs not used: Lainton, Cameron.
ROVERS: Robinson, Lowe, Hanley, O'Connell, Spurr (Jorge 67), Williamson, Evans (O'Connor 46), Cairney, Conway, King (Cham 86), Rhodes (Preston 86).
Subs not used: Raya.
Sent off: Williamson.