The newly promoted Tigers struggled to contain Mourinho's Chelsea in the first half, with the likes of Oscar, debutant Kevin de Bruyne and Eden Hazard dictating proceedings.
The Scottish stopper atoned for his error, though, saving Lampard's effort from 12 yards.
It wasn't long before the Blues made their dominance count, with Oscar stabbing home from close range on 13 minutes to get their season up and running following good link-up play with De Bruyne and Hazard.
Lampard was once again denied by McGregor—this time from close range—but it proved a case of third-time lucky, with the England international smashing home a wonderful free-kick from all of 35 yards.
With Chelsea easing up the intensity, Hull were able to carve out one or two chances of their own but proved no match for the impressive Blues.
Mourinho's return to Stamford Bridge has been one of the summer's most eagerly anticipated fixtures. Here are six things we learned from Chelsea's deserved victory.
Hull City may not be the toughest opposition Chelsea will face this season, but their 2-0 victory over Steve Bruce's men on Sunday doesn't disguise the fact the Blues look primed for an assault on the Premier League this term.
Jose Mourinho's charges appeared fit, ready and, above all else, hungry for success in 2013-14.
They shot out of the traps eager to please their new manager and a 41,374-strong crowd that had been waiting since May to see them in action once more.
Whereas the Blues may have had an air of melancholy about them last term—with events off the pitch damaging things on it—this was an altogether different team. The players had smiles on their faces and the aura was so much different than what we have seen in the past.
The feel-good factor is well and truly alive at Chelsea right now, and it's going to take something special to stop Mourinho's men from marching on to Premier League glory.
Being named as both the club's and players' Player of the Year at the end of last season, it would have seemed ludicrous to suggest Juan Mata would be fighting for his place in the Blues lineup in 2013-14.
After a summer of change at Stamford Bridge, however, it appears very much the case.
The Spaniard was left on the bench against Hull City on Sunday due to a lack of match fitness, but in his place, Chelsea's attacking trio of Oscar, Eden Hazard and debutant Kevin de Bruyne (pictured) looked an exciting proposition.
All three linked up well for Chelsea's opener and terrorized the opposition until De Bruyne was substituted shortly after the hour mark.
The young Belgian was replaced by Andre Schurrle, and the German, also making his competitive Premier League debut, showed signs of what he can offer the Blues this season.
Whereas Mata has been an automatic choice in his first two seasons at Chelsea, on this evidence, that may not always be the case now with the talents Mourinho has at his disposal.
Fernando Torres may not have found himself on the scoresheet against Hull City on Sunday, but the Spaniard will take confidence from knowing he has the faith of his manager, Jose Mourinho.
Picking Torres for Chelsea's opening Premier League fixture was a considerable statement from Mourinho.
The striker hasn't enjoyed a full preseason due to his international commitments with Spain at the Confederations Cup, while fellow frontmen Demba Ba and Romelu Lukaku have heavily featured.
Indeed, the latter has looked particularly impressive after a season's loan with West Bromwich Albion last term, but both he and Ba were forced to watch from the sidelines as Torres started.
It shows who is No. 1 in Mourinho's mind when it comes to his strikers.
It's taken 10 years, but Roman Abramovich has finally addressed Chelsea fans in public.
Ahead of the match against Hull City at Stamford Bridge on Sunday, the club's Russian owner used the matchday program to signal his intent for the future, thanking fans for their support.
In a short statement, he said: "We've had a great decade together and the club could not have achieved it all without you. Thanks for the support, here's to many more years of success."
Since purchasing the club in 2003, Abramovich has never spoken in public. With his address this weekend, it speaks volumes for his commitment to Chelsea.
Jose Mourinho's previous success at Chelsea was built around the talents of Frank Lampard, John Terry, Petr Cech and Didier Drogba.
With the latter no longer at the club, the Portuguese was still able to field three of those four key players in Chelsea's opening game of the 2013-14 season against Hull.
Indeed, Lampard, Terry and Cech were the only surviving members of Mourinho's first game in charge against Manchester United in August 2004, and it seems the Portuguese will be relying on them heavily in his second spell at Stamford Bridge.
It's a wise move, too. The trio have been there, done that and bought several of the T-shirts. With a squad containing so much young talent, Mourinho needs his experienced stars to help them through the campaign if Chelsea are to be successful.
From Sunday's evidence, we'll be seeing and hearing plenty from them this season.
That the three promoted clubs from the championship will struggle in the Premier League is always an easy assumption to make.
After all, they're coming into a league packed full of world-class talent, and for some, it can prove a little overwhelming.
Neither of the Premier League's new teams found themselves on the scoresheet, with the aggregate score totalling 5-0 as Cardiff lost to West Ham United 2-0, Crystal Palace were defeated 1-0 by Tottenham Hotspur, and Chelsea cruised past Hull 2-0.
There's a long way to go, of course, but the signs are already looking ominous.
Garry Hayes is Bleacher Report's lead Chelsea correspondent and will be following the club from a London base throughout the 2013-14 season. Follow him on Twitter here @garryhayes