Pennell scored just six minutes into the match to give Warriors the lead following good work from Heem. Tom Heathcote added the conversion before Micky Young equalled the score for Falcons after patient forward work.
Mike Delaney got the extra two, but Heem, on debut, hit back almost immediately after a chip through from Heathcote fooled the Newcastle defence and the winger snuck in for the score.
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Heathcote nailed the difficult conversion before putting Grove through a gap in midfield, allowing the centre to race away and score, before Delaney grabbed another penalty for Newcastle.
Grove got his second just before half time, but Tom Catterick was in the right place to finish off a Newcastle try to end the half on top.
Catterick then kicked a penalty in the second half, which proved to be the only points in the second 40. Newcastle shored up their defence and a mixture of substitutions and weather slowed the game down to ensure that Worcester left with a vital win.
Newcastle are now bottom of the Aviva Premiership, level on zero points with London Irish, while Worcester move up to sixth.