The Bonus Points
The Toffees centre-back scored 31 in the Bonus Points System (BPS) thanks to his contribution at both ends of the pitch.
Williams scored the winning goal and also registered four clearances, blocks and interceptions (CBI), eight recoveries and two successful tackles.
Left-back Leighton Baines (£5.3m) claimed two bonus points with 28 in the BPS.
He provided three goalscoring opportunities and two crosses from open play, one of which earned the assist for Seamus Coleman’s (£5.5m) first-half equaliser. Baines also produced five CBI, four recoveries and a successful tackle.
Ross Barkley (£7.0m) scored 23 in the BPS to collect the remaining bonus point.
Supplying the cross for Williams's winner, the playmaker also completed three dribbles and weighed in with eight recoveries and two successful tackles.
However, Barkley suffered BPS penalties having been tackled himself on seven occasions.
Arsenal's Alexis Sanchez (£11.8m) also missed out on bonus points despite opening the scoring for the visitors. He was tackled six times and missed the target with one effort on goal.
The ICT Index
Sanchez did, however, top the ICT Index with a score of 12.0.
Producing 13 touches in the Everton penalty area, the Chilean opened the scoring with one of two attempts on goal.
He also created three chances and completed 20 passes in the final third, more than any other player in the match.
Barkley clinched second spot with an Index score of 11.0 He fired one of his three goal attempts on target and created three opportunities, registering as many successful crosses from open play.
The Scout Notes
Coleman’s first-half header continued his fine scoring form under manager Ronald Koeman.
Baines’s assist was his second of the campaign and, as Everton’s designated penalty taker, he could yet emerge as a transfer target.
However, a lack of clean sheets has undermined the potential of both full-backs; Everton have conceded in all but one of the last 12 Gameweeks.
For Arsenal, Sanchez extended his lead at the top of the FPL standings with a 12th goal of the campaign, only one less than his tally for 2015/16.
Theo Walcott (£7.9m) and Alex Oxlade-Chamberlain (£5.8m) retained roles out wide but their second-half withdrawals meant that Sanchez shifted to the flank to make room for Olivier Giroud (£8.6m) up front.
The Gunners missed Mustafi’s presence; they had conceded more than a single goal in a match in only one of the previous 12 Gameweeks with him playing.
Arsene Wenger’s defence has now claimed a single clean sheet in the last nine rounds of fixtures.