did the same teams maintain their dominance in new millennium as well?
Yes
Premier League
The years following 2009 marked a shift in the structure of the "Top Four" with Tottenham Hotspur and Manchester City both breaking into the top four places on a regular basis, turning the "Top Four" into the "Big Six". 
which team has won the epl most times UNANSWERABLE which four teams dominated it in last millennium? Arsenal, Chelsea, Liverpool and Manchester United.
wiki:7765183
Premier League [SEP] Emergence of the "Big Six" (2010s)
The years following 2009 marked a shift in the structure of the "Top Four" with Tottenham Hotspur and Manchester City both breaking into the top four places on a regular basis, turning the "Top Four" into the "Big Six". In the 2009–10 season, Tottenham finished fourth and became the first team to break the top four since Everton five years prior. Criticism of the gap between an elite group of "super clubs" and the majority of the Premier League has continued, nevertheless, due to their increasing ability to spend more than the other Premier League clubs. Manchester City won the title in the 2011–12 season, becoming the first club outside the "Big Four" to win since Blackburn Rovers in the 1994–95 season.