Lock Itoje and flanker Lawes were at the heart of a dominant first-half performance at Twickenham that saw England deny their visitors any meaningful possession and control the territory battle with astute kicking from hand to race into a 17-0 lead.
Ireland fought back somewhat after the break but the hosts held out to secure a 24-12 triumph and keep their 2020 Guinness Six Nations hopes alive – now up to second in the table, behind only unbeaten France.
Lawes was named as the official Guinness Six Nations man of the match after a performance where the stats – powered by AWS – show that he made eight carries for 37 metres and completed 14 tackles, two of them dominant.
And while he was certainly impressed by the 31-year-old, he also lauded the display and leadership of Itoje.
“Maro was really good,” said Jones. “He wants to take a step up as a leader within the team and you do that by influencing better performances by the other players around you.
“He led the way out there and I thought he and Courtney particularly were outstanding.
“Courtney was disappointed with his game against France [in Round 1] and then he only played a little bit against Scotland, so he was ready to play well.
“We gave him the week off last week to freshen him up and he made a hell of a difference out there.”
England’s first-half performance was perhaps as impressive as any produced in the 2020 Guinness Six Nations so far and they have rebounded from that Round 1 defeat in Paris with aplomb – beating Scotland and now Ireland.
Wales are next up in Round 4 and Jones insists his side have reached their full potential yet, despite the effort at Twickenham.
“We played with a lot of control,” added Jones. “We read the conditions well and at half-time, if it was a cricket game, we could have declared!
“I got the preparation wrong for the France game, and I apologised for that, but we were really good against Scotland in difficult conditions.
“We then took a step up here and we will take another step up again for Wales. There’s a lot more to come from us.
“We played tough in the first 40 here but probably took our foot off the gas in the second half. They were always going to get some ball, which they did, but we were disappointed to give away that try at the end and we will need to be better against Wales.”