1709, "to play, sport, frolic;" 1734, "piece of lively play;" perhaps a variant of ramp (v.); but also see romp (n.). Meaning "to win (a contest) with great ease" first attested 1888. Related: Romped; romping.
1734, "piece of lively play," from romp (v.). From 1706 as "a wanton girl" (probably a variant of ramp (n.2)).