Rodriguez whipped Everton in front from the edge of the box, and Michael Keane and Calvert-Lewin ensured it was two wins from two in the Premier League so far this season.
Manchester United climbed two places up to second in the Premier League after Marcus Rashford scored deep into stoppage time to give them a fortuitous 1-0 home win over Wolverhampton Wanderers on Tuesday.
IMAGES from soccer matches played in the EPL, La Liga and Serie A on Tuesday.
Arsenal slumped to a last-gasp 2-1 Premier League defeat at relegation-threatened Brighton & Hove Albion on Saturday in a blow to the London club's chances of securing European football next season. Watford's Craig Dawson grabbed a stoppage-time equaliser with an overhead kick to earn his side a 1-1 draw with Leicester City on Saturday and a vital point in their battle for Premier League survival.
Liverpool moved into the Champions League qualifying spots after a 3-0 win at Burnley on Wednesday took them above Leicester City and into fourth place with one round of Premier League matches remaining.
Images from English Premier League matches played on Sunday.
United down Newcastle after Saints stun Chelsea on a dramatic night in the English Premier League.
Images from EPL matches played on Saturday.
IMAGES from Premier League matches played on Saturday.
IMAGES from the English Premier League matches played on Tuesday
Imperious Liverpool extended their Premier League home winning streak against Arsenal to six on Saturday with an easy 4-0 victory that lifted them to second in the table.
News of all that's transpired on and off the football field