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Henderson struck a first-half brace and then completed his treble in the 56th minute as Thistle went two points clear.
Raith Rovers lost ground after a 2-0 home defeat by fourth-placed Inverness. Alfie Stewart scored twice in the first half at Stark’s Park.
Bottom side Queen’s Park slipped to a 1-0 home defeat against Dunfermline after Rory Macleod’s 18th-minute goal.
A stoppage-time goal from Ryan McGowan saw Livingston get back on track with a 1-0 win over Arbroath, who slipped to a fourth straight league defeat and saw Michael McKenna sent off late on.
Morton’s game against Ayr was postponed because of a waterlogged pitch at Cappielow Park as as Storm Boelo swept through.
League One leaders Ross County kept themselves ahead of Hamilton with a 4-0 win over Airdrieonians after Brian Graham scored a hat-trick.
Hamilton are also on 31 points as they secured a 10th league win, beating strugglers East Fife 2-1.
Montrose moved fourth after a 3-0 win over Peterhead at Links Park.
Cove Rangers against East Kilbride was abandoned after 30 minutes, with the visitors having taken an early lead through an own goal by Jordan White.
In the second round of the Scottish Gas Scottish Cup, Lowland League East side Bo’ness United came from behind to beat Forfar 2-1 at Newtown Park with a late goal from Jamie Allan.
Lowland League West outfit Renfrew pulled off an upset as they beat Stirling 2-1 at New Western Park.
League Two leaders Stranraer avoided an upset as they also recovered from going 1-0 down early against sixth tier Tayport to close out a 3-1 win at Stair Park.
Dumbarton edged past Highland League side Keith 1-0, while Edinburgh City beat League Two rivals Kelty Hearts 4-1 at Meadowbank Stadium.
Marc McNulty scored twice as The Spartans won 2-1 at Lowland League East outfit Lochee United and Elgin City progressed to the next round with a 2-1 win at Stirling University.