England head coach Stuart Lancaster had played down talk of a crisis after defeats to New Zealand and South Africa this month following three consecutive losses against the All Blacks away from home.
The onus was on the hosts to put on a show against a Samoa team whose build-up was disrupted somewhat by reports that players could refuse to play the fixture due to concerns that their union is being mismanaged.
As expected, Lancaster's men proved to be too strong for Samoa as May scored his second and third international tries after getting off the mark against New Zealand in the first November international, but there is still plenty of room for improvement.
George Ford, one of five changes to the side beaten by the Springboks, made an encouraging first start at fly-half as he helped himself to 13 points with the boot and May's performance was another plus.
Mike Brown added England's other try, with all of Samoa's points coming courtesy of Tusi Pisi penalties.
Lancaster would have been expecting his side to put Samoa under pressure from the outset, but it was Samoa who got the first points on the board when Pisi sent over a penalty after England were caught offside four minutes in.
Pisi ought to have made it 6-0 when he failed to send over another penalty, then Ford made no mistake with England's first penalty after the hosts had dominated in the scrum.
May then had an expectant Twickenham crowd on their feet when he took a pass from Brown and showed a rapid turn of pace to score the first try of the game after 19 minutes.
Referee Jaco Peyper asked the video referee to check for crossing and a forward pass from Brown, but the try was awarded and Ford added the extras.
A penalty apiece for either side ensured England led 13-6 at the break and they could have been further in front had Brown managed to cling on to a Ford pass when the hosts had a man over.
Ford had also missed a long-range penalty attempt just before half-time, but he made no mistake just after the interval and then had a major hand in a Brown try that gave England further breathing space.
The fly-half picked out Anthony Watson with a measured cross-field pass and he surged towards the line before offloading to Brown, who crashed over and Ford converted to increase England's lead.
Samoa's hopes of a fightback were dealt a blow when Johnny Leota was sent to the sin bin for a big hit on Ford 11 minutes into the second half and England took advantage with a fine try a minute later.
May once again showed a sharp turn of foot to round off a slick move in which England moved the ball quickly with some impressive handling from Chris Robshaw, Joe Marler and David Attwood in difficult conditions before the wing applied the finish.
Ford was unable to convert and England failed to inflict further damage on Samoa, but will head into next weekend's clash with Australia buoyed by a long-awaited win.