Martinez struck inside two minutes before Domenico Berardi equalised, but Lukaku gave Inter breathing space with a powerful strike and a penalty before half time.
Manchester United were held 1-1 at Wolverhampton Wanderers and missed out on taking top spot in the English Premier League.
List of major transfers in the top Premier League ahead of the 2019-20 season (all transfer fees as reported by British media):
He made it 3-0 with a superb first-time finish into the bottom corner in the 20th minute, scoring his first ever treble in a competitive game, more than 19 years after making his professional debut.
Manchester United continued to splash the cash after Torino announced that Italy full back Matteo Darmian was heading to Old Trafford.
Torino came from behind to beat Serie A leaders Juventus 2-1 in a pulsating derby on Sunday.
Cristiano Ronaldo opened the scoring as Juventus beat visiting Bologna 2-1 on Saturday to move four points clear at the top of the Serie A table. Ronaldo struck from close range after 19 minutes, but Danilo levelled for the visitors soon afterwards.
News of all that's transpired on and off the football field.
The 55 teams have been divided into 10 groups of five or six, and the top two teams in each qualify directly.
The Portuguese forward then fired in the penalty in the sixth minute of stoppage time.
Balotelli was recalled after a four-year absence and given the captaincy for Mancini's first matches in charge in May but the 28-year-old has played only three times for his French club Nice this season and failed to score.
Milan replaced Gennaro Gattuso with former Sampdoria coach Giampaolo during the close season in a bid to improve on last season's fifth place and to take them back to the Champions League.
News of all that's transpired on and off the football field
News of all that's transpired on and off the football field
A round-up of Saturday's action in La Liga, Ligue 1 and Serie A.
News of all that's transpired on and off the football field
A summary of Saturday's action in La Liga, Serie A and Bundesliga.
Real Madrid produced a gutsy performance to earn a 1-0 win at Sevilla, on Sunday, which took them level on points at the top of La Liga
News of all that's transpired on and off the football field
The five-time world player of the year opened his account in the easiest possible fashion by tapping into an empty net from less than two metres in the 50th minute.
First-half goals by Gervinho and Mattia Destro helped AS Roma strengthen their grip on second place in Serie A with a 2-0 win at Chievo Verona on Saturday.
Carlos Tevez scored a stunning goal as Serie A leaders Juventus beat Torino 1-0 on Sunday to continue an extraordinary dominance of their neighbours.
A round-up of Sunday's matches in La Liga, Serie A and Bundesliga.
Brazil midfielder Casemiro stretched Real's advantage right before halftime with a gut-busting run to meet a cross from compatriot Vinicius, but Levante hit back shortly after the interval through former Madrid forward Borja Mayoral.
News of all that's transpired on and off the football field
News of all that's transpired on and off the football field
News of all that's transpired on and off the football field
News of all that's transpired on and off the football field.
News of all that's transpired on and off the football field
News of all that's transpired on and off the football field
A toothless and haggard Real Madrid slumped to a humiliating 10th Liga defeat of the season on Sunday as they lost 1-0 at struggling neighbours Rayo Vallecano.
News of all that's transpired on and off the football field
Raheem Sterling struck twice as the Premier League champions Manchester City beat Crystal Palace 3-1 at Selhurst Park on Sunday to stay within two points of leaders Liverpool.
News of all that's transpired on and off the football field.
Juventus raced into a 2-0 halftime lead after Napoli goalkeeper Alex Meret was sent off in the 25th minute. The visitors then had Pjanic dismissed and Napoli's Jose Callejon pulled one back before Insigne let the Turin side off the hook.
News of all that's transpired on and off the football field
News of all that's transpired on and off the football field
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.
Paulo Dybala came off the bench to give unbeaten Serie A leaders Juventus a 1-0 win away to a brave Bologna side who had the better of the match and hit the post in stoppage time on Sunday.
A summary of sports events and sports persons who made news on Sunday.