Using str_replace so that it only acts on the first match?

There's no version of it, but the solution isn't hacky at all.

$pos = strpos($haystack, $needle);
if ($pos !== false) {
    $newstring = substr_replace($haystack, $replace, $pos, strlen($needle));
}

Pretty easy, and saves the performance penalty of regular expressions.

Bonus: If you want to replace last occurrence, just use strrpos in place of strpos.

Can be done with preg_replace:

function str_replace_first($search, $replace, $subject)
{
    $search = '/'.preg_quote($search, '/').'/';
    return preg_replace($search, $replace, $subject, 1);
}

echo str_replace_first('abc', '123', 'abcdef abcdef abcdef'); 
// outputs '123def abcdef abcdef'

The magic is in the optional fourth parameter [Limit]. From the documentation:

[Limit] - The maximum possible replacements for each pattern in each subject string. Defaults to -1 (no limit).

Though, see zombat's answer for a more efficient method (roughly, 3-4x faster).