Minus the services of talismanic captain Ben Whiteman, out with a 'niggle', but still present at Ewood Park, Doncaster badly lacked his leadership and drive in a one-sided first period, but the spells in the second half were much more to Moore's liking.
Whiteman is the subject of ongoing interest from Barnsley, among others, with the Reds having yet to tempt Rovers into selling their star turn.
Should Whiteman leave, others will have to step up.
A couple of lovely defence-splitting passes from debutant Taylor Richards hinted at quality and there were other positives to garner in the second half, even accounting for the fact that Doncaster relinquished a 2-1 lead as Blackburn imposed their will to triumph 3-2.
The clinching moment arrived nine minutes from time when Adam Armstrong netted from the spot with a first-ever goal from Joe Rankin-Costello nine minutes earlier having restored parity after Doncaster threatened to pull off a shock.
Trailing 1-0 to a fine first-half free-kick from Lewis Holtby, Doncaster turned the tables with Fekiri Okenabirhie's 54th-minute penalty drawing them level before a maiden goal for the club from Madger Gomes put them ahead.
But it was not to be, although Doncaster went down brandishing weapons and with a fair bit of fight.
In the build-up to the game, Moore spoke about how Blackburn had blown off the cobwebs by way of a number of warm-up games, while his own side were still at 'base one.'
The evidence of the first-half heightened those pre-match concerns of Moore, with the visitors looking rusty against a home side who looked stronger, sharper and much more convincing.
Rovers' central midfield axis of Gomes and Richards had their work cut out against the experienced trio of Holtby, Bradley Johnson and Lewis Travis who dominated and Adam Armstrong - linked with a return to hometown club Newcastle - also proved an irritant at the business end.
It was Holtby who made the breakthrough with a delightful curling free-kick as the Lancastrians, handed several promising set-piece situations, finally cashed in on one on the half-hour.
The half was one where Doncaster also created their own problems and when they enjoyed some pockets of possession, they invariably squandered it and badly missed the poise of Whiteman, with Moore's frustration there to see on occasions.
His side's best moment arrived in the opening minutes when Jason Lokilo, making his second debut, was afforded space on the left and his rising shot was blocked by young home keeper Andy Fisher after Blackburn momentarily switched off.
Other than that, Fisher was protected well, with Blackburn comfortably holding sway and the likes of Lokilo, Jon Taylor and Okenabirhie being pretty peripheral figures.
Joe Bursik, making his bow in goal for Doncaster, grasped a deflected low shot from Harry Chapman, while Armstrong hit a free-kick just wide before the pressure told when Holtby broke the deadlock in impressive fashion - although it was his last significant involvement with his afternoon curtailed ahead of the break when he was forced off with injury.
After a limp first half, there were some promising signs that Doncaster had got the message at the break and they were more forceful on the resumption and gave the hosts a bit more to think about.
They forced several corners before a quality move saw Richards' eye-of-a-needle pass find Lokilo, who cut inside before seeing his low shot held by Fisher.
It was better from Doncaster as they were rewarded soon after.
Home captain Darren Lenighan's mistimed challenge on Okenabirhie, who had threatened to get away saw referee Anthony Backhouse point to the spot and the visiting striker - so isolated in the first half - assumed responsibility and coolly sent Fisher the wrong way with an effortless penalty.
The moment certainly shook Blackburn out of their comfort zone, although their response was not immediate.
Lenigan attempted to atone, but put a far-post header over - and it was Doncaster who produced the next telling moment.
Richards again showed his eye for a pass by picking out Lokilo in exquisite fashion before the ball found its way to Gomes, whose low shot crept under Fisher to give Moore's side a lead that they could have scarcely envisaged at the interval.
Despite the scoreline, Moore would have known that the result could hinge on how his side repelled the inevitable spell of pressure from the stung hosts - and Doncaster soon blinked.
Ben Brereton got away down the left and his low cross found Armstrong and amid a rare old scramble after his point-blank shot was blocked on the goalline, Rankin-Costello helped himself to his first-ever Blackburn goal from close in by firing home the loose ball.
Bursik then kept out Brereton's low shot before an entertaining second half took another twist when the hosts were awarded a spot-kick of their own after Brad Halliday brought down Amari'i Bell.
Armstrong sent Bursik the wrong way with Brereton soon having the chance to seal it after the Rovers keeper raced out of goal, but the home forward steering the ball wide of a gaping goal.
Blackburn Rovers: Fisher; Rankin-Costello, Lenihan, Wharton, Bell; Travis, Johnson, Holtby (Rothwell 41); Chapman (Dolan 65), Armstrong; Brereton. Substitutes unused: Eastham, Nyambe, D Williams, Evans, Bennett.
Doncaster Rovers: Bursik; Halliday, Wright, Anderson, John; Richards (Hasani 73), Gomes; Taylor (E Williams 69), Coppinger (Amos 82), Lokilo; Okenabirhie. Substitutes unused: Jones, Greaves, Horton, Blythe.
Referee: A Backhouse (Cumbria).