Overall it was a comfortable win for the Foxes that'll certainly give them a confidence booster for next weeks league clash against a rejuvenated Manchester United side.
In other Premier League action, Jese Rodriguez made a memorable start to life at Stoke by scoring the only goal of a 1-0 home victory over Arsenal.
Mahrez has said he wants to leave but Shakespeare has been pleased with his reaction ahead of the transfer deadline this month.
Clearly intent on pressing home their early advantage, Shakespeare's side then had a golden opportunity to gain the relative comfort of a two-goal cushion.
Leicester took the lead in the first minute as Mahrez danced past two defenders and his strike was palmed away by Matt Ryan to Okazaki who finished. Moving to the English second tier might be a step back for the Nigerian wideman who boasts of experience both at club and country level but it might just be the best solution at least on a temporary basis.
The Seagulls managed to shut out one of the division's most risky sides for 70 minutes before succumbing to a respectable 2-0 defeat.
Albion did have the ball in the net but Glenn Murray was adjudged to be offside.
It was hardly surprising Hughton opted to make a change on the hour and former Leicester winger Anthony Knockaert was given a rousing reception on his introduction.
The Japan international's tap-in owed much to Australia keeper Ryan's fumble and the lead suited a well-versed Leicester game plan as they encouraged the visitors to attack and found them incapable of troubling a sturdy defence.
Leicester: Schmeichel; Simpson, Morgan, Maguire, Fuchs; Mahrez, James, Ndidi, Albrighton; Okazaki, Vardy.
Subs: B Chilwell, D Gray, A King, B Hamer, D Amartey, L Ulloa.
Subs: G Bong, U Hunemeier, J Skalak, N Maenpaa, L Rosenior.