Robinson, who joined from Derby earlier this week, immediately started paying back his £100,000 transfer fee with a first-half header and Husband made sure of the points with an attempted cross that went sailing into the far corner after the break.
Dickov's men were worthy winners and their nerves will be settled as they again aim to establish themselves in the second tier following promotion last year.
While a draw and two defeats from their opening three games is hardly a crisis for Blackburn, Bowyer will be only too aware that he is working for erratic owners who fired three managers last season so he must be understandably anxious to get his first three points of the season on the board.
In truth, it never looked like being here as they were outplayed for the majority of the match, with Jordan Rhodes squandering their best opportunity in the first half.
The hosts' dominance might have been because they have had a clear week owing to Wigan's involvement in the Community Shield last Sunday as there was no sign of rustiness from Dickov's men.
Blackburn defender Tommy Spurr, who joined from Doncaster a few weeks ago, almost laid on an opener for his old team-mates when he sold goalkeeper Jake Kean painfully short with a back pass, but Chris Brown stabbed the ball just wide of the post.
And that dominance was rewarded in the 36th minute when Robinson rose highest from Cotterill's free-kick to nod past Kean.
For all of Doncaster's superiority, Blackburn were not completely out of it in the opening period and Rhodes had their best chance, but he fired wide from an acute angle with home goalkeeper Ross Turnbull stranded.
The start of the second half was a different story completely as, kicking towards their travelling fans, Blackburn laid early siege on Doncaster's goal, forcing a succession of corners which culminated in Chris Taylor heading wide.
However, just before the hour mark they were hit with a sucker-punch as the hosts were the recipients of an outrageous stroke of luck.
Husband was fed the ball on the left and he aimed a cross towards Brown and Robinson in the middle, but over-hit it, sending the ball sailing over the head of Kean and into the top corner to double the lead.
That knocked the visitors right off their stride and Doncaster could have furthered their lead but Brown wasted a golden chance to make it three when he struck a loose ball straight at Kean from eight yards.
Blackburn made a late scramble to get something out of the game and Alan Judge fired two efforts from distance but Turnbull was able to watch them go comfortably over.
Doncaster saw it out with ease and Blackburn left the field to boos from their fans.