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.
Following is a match by match look at the English Premier League's weekend fixtures:
Aston Villa have sacked manager Tim Sherwood, the Premier League club announced on Sunday.
Spain strolled to a 4-1 win at home to Israel, while Italy survived some first-half scares on the way to a 2-0 win and Ukraine registered a 1-0 home win over Ukraine in an action-packed game.
England striker Wayne Rooney has signed a four-year contract extension with Premier League champions Manchester United that will keep their prize asset at the club until June 2019.
Joint-leaders Tottenham Hotspur and Liverpool both dropped points on a busy day of English Premier League action as Leicester City and Southampton narrowed the gap in what is shaping up to be one of the most open title races for years.
England centre back Gary Cahill is so frustrated by a lack of first-team football at Chelsea that he wants to leave the club in an attempt to safeguard his international place at the European Championship in the summer.
Minor league Eastleigh suffered FA Cup heartbreak when they conceded a late equaliser to four-times winners Bolton Wanderers on a gluepot pitch at their snug Ten Acres ground on Saturday.
Manchester United manager Jose Mourinho has promised to show plenty of restraint and respect if he inflicts a first Premier League defeat of the season on his former side Chelsea on Saturday.
IMAGES from the Premier League matches played on Sunday.
Premier League champions Chelsea eased past a disappointing Everton with goals from Spaniards Cesc Fabregas and Alvaro Morata sealing a 2-0 victory on Sunday.
Images from EPL matches played on Saturday.
Luton pulled one back on the half-hour mark when Chelsea keeper Kepa Arrizabalaga failed to keep out Jordan Clark's low effort which squeezed between his hand and leg into the net.
Tim Cahill would love nothing better than to join the select company of Pele, Uwe Seeler and Miroslav Klose by finding the net in a fourth World Cup over the next few weeks but first the Australian actually needs to get on the pitch.
Leicester City manager Craig Shakespeare has said that he never had any arguments with predecessor Claudio Ranieri and there was no ill feeling between the pair prior to the Italian's sacking.
There were a few nerves at the end but Liverpool set up a Champions League semi-final with Spain's Villarreal after Roberto Firmino scored twice in a 3-3 second-leg draw with Benfica on Wednesday to ensure a 6-4 aggregate win.
The Gunners' only league defeat of the campaign was in September away to one of England's traditional top-six clubs, Manchester United, drawing criticism that their strong start to the season was based on wins against lesser opposition.
Real Madrid goalkeeper Keylor Navas says the signing of Belgium keeper Thibaut Courtois has not affected his desire to remain at the triple European champions as he emphatically ruled out leaving the club in order to be assured of first team football.
Match-by-match facts and statistics ahead of the Premier League fixtures on April 28-30
Images from the EPL match played between Manchester United and Watford on Sunday.
Of the 220 players who started for Premier League clubs at the weekend, only 73, or 33.2 per cent, were eligible to play for England.
The United fans, who celebrated the victory at the end of the game with the manager and players, have not been the source of criticism of Solskjaer -- indeed the Norwegian has enjoyed strong backing from supporters who attend games at Old Trafford and those who travel away.
Images from the English Premier League matches played on Saturday
Manchester United midfielder Marouane Fellaini believes he was made the scapegoat for the team's torrid time under former manager David Moyes in the Premier League last season.
Premier League leaders Manchester City won their derby with United 3-1, while Liverpool kept pace with a home win over Fulham.
'We want to thank him (Costa) for what he did with this club. We wish him all the best for the future'
Juergen Klopp has said his Liverpool team must be prepared to play ugly football to secure Champions League qualification following the injury to productive forward Sadio Mane ahead of Wednesday's Premier League clash against Bournemouth.
Former France winger David Ginola will announce on Friday that he is entering the race to become president of world soccer's governing body FIFA, The Sun reported on Thursday.
Chelsea were given a stiff examination by Stoke City at Stamford Bridge on Saturday before extending their lead at the top of the Premier League.
Ellen White scored her fifth goal of the tournament in between Jill Scott's opener and a Lucy Bronze screamer from the edge of the area as Phil Neville's side set up a mouthwatering clash with either holders the United States or hosts France.
Striker Costa ends second spell at Atletico Madrid.
Under-fire Jose Mourinho had been on the verge of delivering the perfect response to his critics on Saturday with Manchester United closing in on a second consecutive comeback win, at the home of his old club Chelsea to boot.
'This award is not just mine.' 'It is my team mates' from Real Madrid and Croatia.' 'Without my coaches, I would not have won this and without my family I would not be the player I am today.'
As the black-tinted sports cars carrying Manchester United's millionaire footballers rolled into the club's Carrington complex for the start of pre-season training on Wednesday, no one wound down any windows to discuss the start of life under Jose Mourinho. But there was surely only one topic of conversation when the players began the hard task of proving to the new manager on the pitch that they can forge the sort of future he outlined so eloquently at his news conference the previous day.
News of all that's transpired on and off the football field
Playing spectacular football is all well and good but Manchester United must find the right balance in both areas of the pitch if they want to be successful this season, manager Louis van Gaal has said.
News of all that's transpired on and off the football field
Images from the English Premier League matches played on Tuesday
Images from the FA Cup matches played on Saturday
The following are talking points from the weekend's Premier League action:
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