How do we reconcile the prohibition of self-praise with the command to purify oneself?

There is no contradiction between the two verses. The meaning of the first verse, "So do not تزكوا yourselves" (وَلَا تُزَكُّوا أَنْفُسَكُمْ), is "do not praise yourselves and give thanks to yourselves." It prohibits self-commendation through praise and lauding, due to the hypocrisy, arrogance, and boasting involved therein.