Peter Weatherson struck a late equaliser for Morton as bottom-of-the-table Queen of the South were pegged back twice.
Scott McLaughlin opened the scoring for the visitors after only two minutes, firing home left-footed following Daniel Carmichael's right-wing cross.
Andrew Jackson equalised for the hosts 15 minutes later with a close-range finish from Grant Evans' flicked header.
Morton keeper Dominic Cervi then denied Carmichael's 20-yard effort before the visitors regained the lead 12 minutes after the restart.
Kevin Holt's ball from the left found Stephen McKenna and he drilled a stunning strike into the top-right corner from 35 yards.
It remained for Weatherson to have the final say as he slotted in Archie Campbell's cross to seal a point for his side eight minutes from time.
Morton: Cervi, McCann (Fitzharris 71), O'Ware, Smyth, Evans, Derek Young, Di Giacomo, McGeouch, O'Brien, MacDonald (Weatherson 76), Jackson (Campbell 76). Subs Not Used: Deans, Graham.
Goals: Jackson 17, Weatherson 82.
Queen of South: Robinson, Craig Reid, Higgins, McKenna, Black, Holt, Johnston (Simmons 86), McLaughlin, Carmichael, Brighton, Smith (McCusker 73). Subs Not Used: McKenzie, Alan Reid, Clark.
Goals: McLaughlin 2, McKenna 57.
Ref: William Collum