Midfielder Sanchez won the Top Points Scorer award with an unrivalled total of 264 points, helped by 24 goals, 11 assists and 32 bonus points.
Alli claimed the Best Under-21 Player award after playing a pivotal role in helping Spurs finish second in the Premier League for the first time.
The 21-year-old was the sixth-highest goalscorer in the division with 18 goals, and he also produced 11 assists. Only Sanchez accumulated more FPL points than his 225.
The Fan Favourite award went to Manchester United goalkeeper David De Gea, who averaged a 37.4% ownership across the season and totalled 136 points, while fellow goalkeeper Tom Heaton of Burnley was also honoured for making a FPL high 142 saves.
Romelu Lukaku's (£10.1m) outstanding performances for Everton earned him the Biggest Price Increase award, the Belgian striker netting 25 goals to gain £1.1m in value after starting the season priced £9.0m.
Alexis Sanchez (MID, Arsenal) 264pts
Dele Alli (MID, Tottenham Hotspur) 225pts
David De Gea (GKP, Manchester United) 37.4%
Romelu Lukaku (FWD, Everton) £1.1m+
Tom Heaton (GKP, Burnley) 142 saves