His Hull City side - who came into this game on the back of illuminating if contrasting Championship victories over Blackburn Rovers and Sheffield Wednesday - have yet to record a trio of successive wins under his watch.
It is something the club last achieved in January 2022 in his predecessor Shota Arveladze’s maiden match in charge and in Acun Ilicali’s first home appointment as City’s new owner and the wait goes on.
There will have been disappointment here on a night when the hosts could have moved joint top with another three points. It is only late August, but it would have been a good public relations exercise by those in amber and black if that had been achieved.
But it should be tempered by some relief. For fair spells, the hosts were second best to a Bristol City side who did former Hull chief Nigel Pearson proud on the week of his milestone 60th birthday.
Despite being without a number of players, they had Hull on the back foot for fair spells and were relentless in their work ethic - regrouping after the Tigers afforded themselves the fillip of another handsome strike to put them on their way from Ozan Tufan on 17 minutes.
It was as good as it got for Hull, who would eventually be pegged back by that ageless raider Nakhi Wells. There were some chances late on, but substitute Aaron Connolly could not repeat his recent feats.
On the balance of play, this was still a point gained and Rosenior will appreciate that. His side's defensive resolution, amid some serious pressure, was admirable.
A discernible air of expectation greeted Hull ahead of kick-off and all was set fair after 25 minutes, with the Tigers - well-oiled, front-foot and confident - looking the part.
The cherry arrived by virtue of an opener, with Tufan again showing his penchant in front of goal with a deadly finish to follow on from his treble against Sheffield Wednesday.
His crisp first-time finish was emblematic of his current sense of well-being. That he was able to sweep the ball home owed much to the sterling work of City's unsung hero this season in Liam Delap.
The indefatigable loanee dropped his shoulder on the wing to beat Zac Vyner and his cross set up the Turk on a plate.
Hull were starting to fancy it and it was looking reasonably easy. Too easy with the hosts perhaps lulled into a false sense of security.
Rosenior had spoken beforehand about the need to maintain concentration and avoid sloppiness. His words were not heeded.
The Robins seized on the hosts indecision and assumed the box seat.
Somehow, it would remain 1-0 at the break with Hull even going close to increasing their lead when Alfie Jones’s header was helped onto the post by Max O’Leary following a fine bending free-kick from Scott Twine.
That the visitors did not boast an advantage themselves was head-scratching.
It was partly due to the last-ditch qualities of Sean McLaughlin and Jacob Greaves in getting in the way of goalbound efforts of Wells, Mark Sykes and George Tanner.
Fortune also played a significant part with Sykes blasting off target from close range when it looked easier to score and Joe Williams firing over a beckoning empty net after City coughed up possession and were opened up.
Then at the end of the half, an assistant referee would intervene, albeit tardily, with an offside flag, after Wells wheeled away in celebration after netting a rebound.
The Robins did not let up when handed a party invite. Their start to the second half reinforced that, but fortunately, their finishing was still off beam, with Jason Knight planting a free header wide.
The early enthusiasm of the home support was understandably dimmed. There was concern and it intensified when the West Country outfit equalised. Even if it was an inevitable development on the balance of play.
Something had to give and it did and Wells really couldn’t miss at the far post following a pinpoint low cross from Sykes, although he gave Greaves the slip too easily.
Wells should have been hailing a second minutes after, but Ingram saved the day with Hull looking increasingly spooked.
A brief spot of respite saw Twine exhibit the set-piece prowess he is renowned for. O’Leary was equal to his well-placed curler and soon raced to make an even better save to stop Connolly from continuing his recent purple patch when sent clear.
Connolly missed another chance late, while Harry Cornick was denied by Ingram. There was no late twist, unlike the last two fixtures between these sides here.
Hull City: Ingram; Coyle (Christie 89), Jones, McLoughlin, Greaves; Slater, Seri; Traore (Vaughan 76), Tufan (Estupinan 61), Twine; Delap (Connolly 61). Unused substitutes: Lo-Tutala, Vinagre, Allahyar, Simons, Smith.
Bristol City: O’Leary; Tanner (Gardner-Hickman 76), Vyner, Naismith, Pring, James, Williams, Knight; Sykes (Mehmeti 90), Wells (Cornick 76), Bell (Weimann 77 (Roberts 80)). Unused substitutes: Bajic, King, Yeboah.
Referee: J Linington (Isle of Wight).