Anderson beat James Wade 7-3 to join Van Gerwen and Peter Wright in the last four.
Taylor's 7-3 win over the PDC world champion kept him fourth in the table, two points clear of Dave Chisnall.
The 56-year-old will qualify for the play-offs if he avoids defeat by Adrian Lewis in Aberdeen.
However, a narrow loss on 11 May should also be enough for the 16-time world champion to go through as he has a vastly superior leg difference to his fellow Englishman.
Van Gerwen, who is hoping to finish top of the Premier League table for the fifth year in succession, remained a point clear of second-placed Wright despite his loss to Taylor.
Wade had already been eliminated with his loss to third-placed Anderson, while Taylor's victory ended the play-off hopes of Lewis and Raymond van Barneveld, who lost to Wright and Chisnall respectively in their penultimate group matches.
Peter Wright (Sco) 7-2 Adrian Lewis (Eng)
Raymond van Barneveld (Ned) 5-7 Dave Chisnall (Eng)
James Wade (Eng) 3-7 Gary Anderson (Sco)
Michael van Gerwen (Ned) 3-7 Phil Taylor (Eng)
Phil Taylor beat Michael van Gerwen in Sheffield to close in on a Premier League play-off spot, while Gary Anderson secured his semi-final berth.