In Classical Latin, purpose would normally be expressed with ut, or ad with a gerund, or a supine with a verb of motion, or numerous other ways.
However, in later and vulgar Latin (most notably the Vulgate Bible), a bare infinitive could be used instead. The most famous example is probably from the apocryphal Acts of Peter: Saint Peter is fleeing persecution in Rome when he meets Jesus, and asks quō vādis, Domine? ("where are you going, Lord?"). Jesus replies, ad Rōmam eō iterum crucifīgī ("I'm going to Rome to be crucified again").
When did this arise, and when did it catch on? To my understanding, it doesn't appear in the vulgar Latin of Plautus, who prefers the supine.