I know that if you sacrifice your commander to rescue from the underworld and send it to the command zone that it'll still find your commander and return it to the field on the next upkeep. But what if you sacrifice someone else's commander.
Say you've taken control of your opponents commander with new blood and sacrifice it to Rescue a creature from your graveyard. The commander would go back to its owner's command zone but would you get it back with the creature you've rescued?
Even here, the sacrificed commander card will get to return to the battlefield under your control, regardless of who owns that card. All that matters for the commander card to come back in this case is that the card was moved to a public zone, such as the command zone (C.R. 400.7h, 400.2), and that card didn't leave that zone (C.R. 400.7). (Note that a commander that would go to the graveyard goes to the command zone instead only if its owner makes that decision; the commander doesn't automatically land there in that case [C.R. 903.9].)
The rules for the Commander variant changed with Core Set 2021 in a way that materially affects this answer.
The answer is now: In general, only if the commander's owner chooses to leave the commander in their graveyard and it doesn't leave that graveyard before Rescue from the Underworld returns it to the battlefield.
Now, in general, if a commander is sacrificed with Rescue from the Underworld, it will go to the graveyard as normal (C.R. 701.17a). And soon after it lands there, a state-based action gives its owner the option to move their commander from the graveyard to the command zone (C.R. 903.9a). If the commander moves to the command zone this way, however, Rescue from the Underworld won't bring that commander back to the battlefield, since it has left the graveyard (C.R. 400.7, especially C.R. 400.7h). The commander will return this way only if it hasn't left the graveyard in the meantime.
EDIT (Jul. 26, 2021): Clarification. One rule was renumbered in the meantime.
Say you've taken control of your opponents commander with new blood and sacrifice it to Rescue a creature from your graveyard. The commander would go back to its owner's command zone but would you get it back with the creature you've rescued?
Even here, the sacrificed commander card will get to return to the battlefield under your control, regardless of who owns that card. All that matters for the commander card to come back in this case is that the card was moved to a public zone, such as the command zone (C.R. 400.7h, 400.2), and that card didn't leave that zone (C.R. 400.7). (Note that a commander that would go to the graveyard goes to the command zone instead only if its owner makes that decision; the commander doesn't automatically land there in that case [C.R. 903.9].)EDIT (Jul. 2, 2020): See comment 3.
The answer is now: In general, only if the commander's owner chooses to leave the commander in their graveyard and it doesn't leave that graveyard before Rescue from the Underworld returns it to the battlefield.
Now, in general, if a commander is sacrificed with Rescue from the Underworld, it will go to the graveyard as normal (C.R. 701.17a). And soon after it lands there, a state-based action gives its owner the option to move their commander from the graveyard to the command zone (C.R. 903.9a). If the commander moves to the command zone this way, however, Rescue from the Underworld won't bring that commander back to the battlefield, since it has left the graveyard (C.R. 400.7, especially C.R. 400.7h). The commander will return this way only if it hasn't left the graveyard in the meantime.
EDIT (Jul. 26, 2021): Clarification. One rule was renumbered in the meantime.