This　paper　investigates　the　pth　moment　exponential　stability　of　impulsive　stochastic　delayed　systems　(ISDS).　New　stability　criteria　for　ISDS　are　developed　by　applying　the　Razumikhin　approach　and　a　novel　concept　of　average　random　impulsive　estimation　(ARIE).　Stochastic　impulsive　strength,　the　time-varying　delay　in　continuous　dynamics,　and　the　impulsive　delay　are　considered　simultaneously,　and　there　are　no　imposed　restrictions　on　their　sizes.　Utilizing　ARIE,　the　proposed　control　scheme　with　stabilizing　impulse　can　still　ensure　the　stability　of　the　whole　system　under　the　presence　of　impulsive　perturbations　at　some　impulsive　instants,　that　is,　it　allows　some　impulsive　intensities　at　impulsive　instants　are　greater　than　1　or　a　certain　threshold　which　is　more　than　1.　In　addition,　the　requirement　for　the　sign　of　time-derivative　of　Razumikhin　function　is　also　relaxed.　Several　illustrated　examples　are　given　to　verify　the　effectiveness　of　our　proposed　results.　©　2024　Elsevier　Ltd