England somehow ran in five tries but they created little of note in attack and although Johnson will be happy to have banked two points, the laboured display will have done nothing to soothe his furrowed brow.
His side went into the game on the back of five defeats in six matches and Johnson decided experience and a more conservative approach was the order of the day, with the solid Goode and Cueto recalled after long absences.
In contrast Italy boss Nick Mallett decided to gamble by picking the older of the Bergamasco brothers, Mauro, normally a flanker, at scrum-half because they had lost their three leading number nines to injury.
The move was to backfire in spectacular fashion.
Bergamasco is a fine open-side with 69 caps to his name but his inexperience at number nine cost his side a try within two minutes of the kick-off.
The Stade Francais player was - like a good number seven - unable to resist the temptation to clear out English players at a ruck and when the ball fell loose he was not there to control it.
Watch as Bergamasco has a shocker at scrum-half for Italy
England kicked through to within 10m of the Italian line and when Saracens hooker Fabio Ongaro overthrew at the resulting line-out for the visitors, Goode collected and set up great field position.
Nick Easter and James Haskell both had a crack and when England recycled for a third time Goode chipped through and won the race to touch down.
Goode converted but spurned the chance to extend the lead when he missed two kickable penalties.
Italy also failed to take their first chance, Andrea Marcato missing a penalty for the visitors, and they shipped a second try after 18 minutes following a second Mauro Bergamasco error.
Italy once again lost control of the ball at the base after Bergamasco had been sucked into a ruck and Haskell's flick saw Ellis scamper 20m to the line and dive over for an unconverted try.
It then went from bad to worse for Bergamasco as his horrendous pass eluded Gonzalo Garcia and Goode kicked ahead before Flutey gathered the ball and went over.
Goode's conversion put England 19-0 ahead and Mallett's gamble had resulted only in England filling their boots.
There was plenty of commitment in defence but neither side impressed in attack
The visitors finally managed to get on the board late in the first half with two penalties from McLean, on for battered fly-half Marcato, either side of a Goode penalty for the hosts.
That meant England led 22-6 at half-time and Italy finally accepted the inevitable, removing Mauro Bergamasco and bringing on Giulio Toniolatti for just his second cap.
With a healthy lead and Italy in disarray it was all set up for England to open up in the second half, but they never really got going.
Ellis marked an effective display by having the pace to go over from halfway after England had turned over Italian possession, with Goode's conversion making it 29-6.
Italy claimed their solitary try as Mirco Bergmasco finished off a sweeping move after 72 minutes to cap a mixed day for the Bergamasco brothers.
Cueto, playing for England for the first time since the 2007 World Cup final, then rounded off the scoring with a 78th-minute try.
But the fact the hosts scored five tries in the Six Nations for the first time in three years said much more about Italy's flaky display than it did about England's attacking prowess.
England: D Armitage; Sackey, Noon, Flutey, Cueto; Goode, Ellis; Sheridan, Mears, Vickery, Borthwick, Kennedy, Haskell, S Armitage, Easter.
Replacements: Hartley for Mears (55), Foden for Ellis (60), White for Sheridan (60), Geraghty for Flutey (60), Worsley for Armitage (62), Croft for Kennedy (73), Tait for Noon (73).
Sin-Bin: Haskell (34), Geraghty (63).
Italy: Masi; Robertson, Canale, Garcia, Mi Bergamasco; Marcato, Ma Bergamasco; Perugini, Ongaro, Castrogiovanni, Dellape, Bortolami, Sole, Zanni, Parisse.
Replacements: McLean for Marcato (29), Toniolatti for Ma Bergamasco (41), Pratichetti for Garcia (55), Reato for Bortolami (55), Festuccia for Ongaro (55), Nieto for Perugini (60), Montauriol for Dellape (76).
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