Steven Anderson and Stevie May score the goals as St Johnstone beat neighbours Dundee United 2-0 at McDiarmid Park.
Aaron Taylor-Sinclair's late header sealed a vital three points for Partick who beat Kilmarnock 2-1 at Rugby Park.
Hibernian are firmly embroiled in the battle to avoid the relegation play-off spot after a 2-0 defeat away to St Mirren.
Jamie Hamill scored a penalty and was later sent off as Hearts beat Ross County 2-0 at Tynecastle.
John Sutton grabbed a late equaliser as Motherwell drew 3-3 with champions Celtic at Fir Park.