Buttler brought up his sixth first-class hundred – and only his second in five years – on the final morning of the three-day practice match against New Zealand A as England were all out for 405, a first-innings lead of 103.
Archer’s pace ruffled a number of batsmen as he and Sam Curran collected three wickets apiece to put England within sight of victory.
But a battling ninth-wicket rearguard from William Somerville and Ajaz Patel snuffed out the chance of a result.
The home side had lurched to 129 for eight before tea at Whangarei but Somerville (32 not out from 87 balls) and Patel (10 not out off 67) resisted England’s best efforts for 22.4 overs before the teams shook hands with a little less than hour remaining, with the locals 169 for eight.
Ultimately, while Archer proved a handful on an unresponsive pitch, and Curran produced the odd bit of movement as wind swept across the Cobham Oval, England were unable to make inroads with the ageing ball.
This was a good workout, though, for an XI that, will almost certainly take the field in the first Test against the Black Caps at Mount Maunganui on Thursday, fitness permitting.
A stalemate was also probably a fair result, given the hosts had charitably declared their first innings on 302 for six.
Captain Tom Blundell may have been ruing that decision as his side struggled when attempting to wipe out the first-innings deficit.
Tim Seifert’s promotion to opener following Hamish Rutherford being withdrawn because of concussion lasted just two balls as Archer induced the edge and Dom Sibley took a sharp chance to his right at third slip.
Fellow opener Rachin Ravindra departed in identical fashion, and although Glenn Phillips survived a sharp burst from Archer, the first-innings centurion was caught down the leg side by keeper Buttler off Curran for 36 on the stroke of lunch.
The wheels fell off on the resumption as 70 for two before Phillips’ dismissal became 104 for seven.
Curran produced some pleasing movement to take the ball away from Jimmy Neesham, who briefly stood his ground after Buttler dived to his left to pouch a low edge but departed after accepting the England gloveman’s word.
Daryl Mitchell played around a straight one from Stuart Broad and was trapped in front, while Blundell could not take advantage of a drop from Joe Root as he compulsively pulled Archer to Sibley in the deep.
Jamieson aimed a slog at Ben Stokes but spooned the ball straight into the air, leaving Buttler with a simple catch before Root spilled another chance at first slip to reprieve Scott Kuggeleijn.
Curran had his third wicket when he bowled Kuggeleijn to leave the hosts 26 ahead with only two wickets in tact.
England found Somerville and Patel in a defiant mood, the pair putting a premium on their wickets as the tourists rotated their attack, with only Archer giving the batsmen fleeting cause for concern.
Root brought himself on after frontline spinner Jack Leach proved ineffective.
But when the England captain momentarily left the field, deputy Stokes had seen enough, with New Zealand A on 169 for eight.
Buttler had earlier been content to nudge his way to the 12 runs he needed to reach three figures from 141 balls before demonstrating his brute strength with a monstrous straight six off Somerville.
He departed for 110 after gloving a pull from Kuggeleijn to wicketkeeper Blundell to end a 71-run stand for the ninth wicket.
Broad slapped the next ball to midwicket to leave Archer stranded on 41.
A total of 10 Pakistan players tested positive for Covid-19.
The Antigua-born seamer is itching to make a big impression in the three-Test series in England that starts in Manchester on July 8.
The 21-year-old says the route from British Asian hubs to the county game can be “daunting”
On arrival in England the squad will head to Blackfinch New Road.
Sheyne Moseley, Shane Dowrich and Shamarh Brooks registered half-centuries at Old Trafford.
The Kent batsman has won four Test caps.
The duo shared an unbroken stand of 131 before lunch on day three.
Archer initially stayed away from the get together after he reported a member of his household feeling unwell on Tuesday.
West Indies Test captain Jason Holder declined to bowl for the third day in a row.