Updating PowerEdge T620 BIOS/firmware with no OS installed on hardware yet

So I'm setting up a new VMWare ESXi host for a client and before installing VMWare I was wanting to update the BIOS. Server currently has 1.3.6 installed but 1.4.6 is available on drivers page, so I figure hey might as well update the BIOS before anything's installed so it can't break anything down the road. I'm a bit new to this and all of my other clients who have Dell servers have Windows installed on the box so it's always been quite easy to update the BIOS--just download the Windows update package, run that, and reboot; simple. But this appears to be a bit trickier. I tried booting the server (which currently has no OS installed) to the Dell OMSA 7.1 centOS live CD, and from there I downloaded the BIOS file (the RedHat bin file version) and executed that file with root privs from command line "~sh T620_BIOS_filenamesomething.bin". It appeared to finish and asked me if I wanted to reboot. I chose Y, but when the server rebooted, I still see 1.3.6 in the BIOS.

So I'm wondering if I performed a BIOS update in a non-supported way that appeared to work at first glance, but actually did not.

I'm having a tough time finding Dell documentation on how to update a server BIOS when the server's NOT running Windows. Seems to me that this type of setup (VMware/Hyper-V installed on the hardware) is only going to be more and more popular going forward, so hoping to get a known-working (and supported) process for doing this. I'm also thinking that upgrading the other firmware on the server will involve a similar method of doing so, so really hoping to figure this out.

Any pointers? Thanks much!