The hosting Pilgrims started the brighter of the two sides and could have taken the lead in the sixth minute when Conor Hourihane sent over a free kick for Curtis Nelson, but the defender headed over the target.
That goal prompted a positive reaction from Guy Whittingham's visitors and with 35 minutes played Plymouth goalkeeper Luke McCormick was forced to dive full stretch to tip over John Marquis's shot from distance.
However, four minutes later McCormick was beaten. The ball broke for Wallace on the edge of the area and the 19-year-old sent a half-volley beyond the reach of the Plymouth stopper.
The home side finished the half in the ascendancy, but both Reuben Reid and Nelson spurned chances.