Taking the reins following Steve McClaren's ill-fated spell at the City Ground, Cotterill enjoyed a dream start courtesy of a surprise midweek win over high-flying Middlesbrough.
Forest followed that up on Saturday by claiming three more Championship points once more thanks to Majewski's late goal, which came after Kevin Phillips had cancelled out Wes Morgan's opener.
Guy Moussi was sent off with eight minutes remaining to set up a tense finish but Forest held on, much to the delight of Cotterill.
Buoyed by their midweek success, Forest started impressively and enjoyed the majority of the early possession.
Despite their dominance, opportunities were still at a premium, so much so that the first effort on goal did not come until the 21st minute.
Lewis McGugan delivered a typically dangerous set piece and, after rising highest in the area, Luke Chambers headed just over.
Chambers was again causing problems moments later, capitalising on a poor clearance to volley narrowly wide.
The one-way traffic continued thereafter, with opportunities proving increasingly frequent as Ishmael Miller saw his deflected effort saved by Matt Gilks.
Blackpool, though, did start to come back into encounter as the half-time whistle drew nearer, with Morgan having to be on high alert to clear Jonjo Shelvey's wicked cross.
The defender was then on hand to make an even bigger contribution, giving Forest the lead in the 39th minute.
After McGugan's corner found its way back into his path, the winger sent in a delicious centre which Morgan headed home.
However, the opener served only to wake the Tangerines up and they restored parity almost immediately through Phillips.
The former England striker showed all his class to net his sixth goal of the season by beating Lee Camp with an excellent 25-yard effort.
Despite heading into the break in the ascendancy, Ian Holloway's men struggled after the interval as the visitors again enjoyed the better of proceedings.
Set-pieces were proving Forest's main weapon once more as Chambers headed another excellent McGugan corner over.
It was Blackpool who enjoyed the better of things thereafter, though, and they almost went ahead in the 75th minute when Thomas Ince hit the post.
But, just as the were building up a head of steam, the Tangerines were hit with a sucker punch as Majewski's half-volley beat a seemingly unsighted Gilks.
Forest's cause was then not helped by Moussi picking up a second booking, but they held on to win - thanks in the main to an excellent save from Camp, who denied Ian Evatt in the dying minutes.