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.
A summary of Sunday's Premier League matches
Monaco owe most of their recent success to their young guns, but when they face Manchester City looking to overturn a two-goal deficit in their Champions League last-16 tie on Wednesday, they will turn to a more experienced player in Radamel Falcao.
IMAGES from the English Premier League matches played on Sunday
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.
Manchester City boss Pep Guardiola has warned his side to beware of Monaco's "killers in the box" when they host the principality club in the first leg of their Champions League, last 16 tie on Tuesday.
IMAGES from the English Premier League match played on Saturday
IMAGES from Saturday's English Premier League matches.
In Pep Guardiola's 100th match in charge of the Manchester club, captain De Bruyne led from the front as City outclassed the Gunners, who have now suffered six home games without a win. Images from the EPL matches played on Sunday.
Images from the EPL matches played on Saturday
Photos from the UEFA Champions League last 16 first leg-matches played on Wednesday
Premier League leaders Manchester City turned on the style with a 3-1 win over Manchester United in their derby clash, on Sunday, leaving Pep Guardiola's unbeaten side two points clear of Liverpool.
IMAGES from the English Premier League matches played on Tuesday
IMAGES from the English Premier League matches played on Saturday.
Images from the Champions League round of 16 second leg matches played on Tuesday
Liverpool had to be satisfied with a 1-1 Premier League draw at Arsenal on Saturday as their usually prolific attacking trio were well shackled by their improving hosts.
IMAGES from Saturday's English Premier League matches.
An inexperienced Germany suffered an embarrassing 3-1 defeat to Slovakia in a storm-affected friendly ahead of Euro 2016.
Isco scored in the sixth minute of stoppage time as Spain launched an improbable fightback to snatch a 2-2 friendly draw against England with both their goals coming after the 89th minute at Wembley on Tuesday.
News of all that's transpired on and off the football field
Images from Champions League matches played across Europe on Tuesday
Two late goals in two minutes from Sergi Roberto and Luis Suarez gave European champions Barcelona a dramatic 2-1 win over Bayer Leverkusen in the Champions League on Tuesday.
Cristiano Ronaldo renewed his personal battle with Lionel Messi by scoring his 71st Champions League goal, putting him three behind the Argentine's newly-set record, in Real Madrid's 1-0 win at FC Basel on Wednesday.