The flaws, found by researchers at Core Security, affect OpenView Network Node Manager versions 7.51, 7.53 and 7.53 with the NNM_01195 patch.
HP is urging customers to visit its web site and download the new patches.
Network Node Manager allows administrators to monitor network system events remotely and carry out performance monitoring.
The first flaw is a stack-based bug which was found to be vulnerable despite an earlier patch. The other two are heap-based buffer overflows in two sections of the code.
The bugs would allow remote code execution on infected systems and, given the broad capabilities of Network Node Manager, would allow a hacker full access to compromised systems.
"While remote network management technologies offer substantial value in terms of allowing organisations to maintain constant vigilance and control over their networks, the flipside is that attackers can potentially use available vulnerabilities in these systems to wreak havoc on internal infrastructure," said Ivan Arce, chief technology officer at Core Security.
"It is vitally important for remote systems management solution providers to minimise these easily exploitable security flaws that can allow for remote system compromise."
A researcher at Core discovered the flaws in January and has worked with HP to develop the patches before releasing the news.