Everton signed Dele Alli from Tottenham in February for a fee that could reach £40m
Manager Frank Lampard had warned of another Premier League relegation battle after two disappointing defeats in the United States with no goals scored and six conceded.
Everton only secured Premier League safety last season in their penultimate game.
The Toffees' Vitalii Mykolenko and Tom Davies scored in the first 11 minutes.
Championship Blackpool pulled one back before half-time through Gary Madine.
Former Tottenham and England midfielder Alli, 26, made it 3-1 after the break before Callum Connolly pulled a goal back for the Seasiders. Alli's close-range second on 63 minutes finished the game.
Sunday's victory came three days after a 4-0 defeat by Major League Soccer side Minnesota United, following a 2-0 loss to Arsenal in the first game of their US tour.
A small number of fans have been protesting outside Goodison Park this weekend to highlight what they claim is the "mismanagement" of the club under owner Farhad Moshiri.
Moshiri recently ended takeover negotiations and insisted the club is not for sale.
Meanwhile, newly-promoted Fulham won 3-1 against GD Estoril Praia in the final game of their pre-season trip to Portugal.
Aleksandar Mitrovic - who set a Championship record with 43 goals last season - scored two headers, before new signing Joao Palhinha got his first goal for Marco Silva's side.
--- Courtesy of BBC Sport