Hamilton had threatened to continue their recent revival with a bright start but all hope was extinguished when Mark McLaughlin was sent off for bringing down Andy Jackson.
Craig slotted home the resulting penalty in the 29th minute and Hamilton's spirit could not make up for their numerical disadvantage.
Tomas Cerny later saved Craig's second penalty - the 15th Accies have conceded this season - but their relegation was confirmed by St Mirren's 1-0 win at Aberdeen.
Hamilton had taken 10 points from their previous four games to cut their deficit on St Mirren from 12 points to three and they threatened to continue their recent revival in the opening stages.
Nigel Hasselbaink slotted home within a minute of kick-off but was flagged offside after Simon Mensing delayed his pass with Hamilton outnumbering the home defence.
The visitors soon had another great chance when Dougie Imrie crossed for Jon Routledge, but Peter Enckelman dived to save the on-loan Wigan player's header from 10 yards.
Saints, on the back of away wins over Hibernian and Aberdeen, soon settled and Liam Craig twice found himself in good positions but failed to get enough power on an attempted lob from and then took a heavy touch.
Craig was soon foiled by an excellent covering tackle from David Buchanan following Andy Jackson's cutback, and Peter MacDonald blazed the loose ball over the bar.
St Johnstone continued to push and Cerny saved from team-mate Gary McDonald and Jamie Adams as the hosts threatened from two corners.
Accies were soon back on the attack with Enckelman diving to save Hasselbaink's 20-yard shot before Jim McAlister headed wide following Imrie's cross.
But their SPL status suffered a fatal blow when McLaughlin was beaten for pace by Jackson after MacDonald had headed on a long ball.
The centre-back slid in to bring Jackson down with referee Steve Conroy awarding a penalty and showing a red card, the seventh of Hamilton's SPL campaign.
McLaughlin pointed at the referee's assistant as he complained about the outcome, apparently claiming the offence occurred just outside the box.
But McLaughlin was trudging down the tunnel when Craig sent Cerny the wrong way from the spot.
Alex Neil dropped back into central defence before Billy Reid brought on David Elebert for David Buchanan, to a chorus of boos from the travelling fans, and switched to a 3-4-2 formation.
Although Hamilton went on to enjoy their fair share of possession, they could not get in behind the Saints defence.
Reid again changed formations to a 4-4-1 after half-time and Imrie and Hasselbaink both caused their opponents problems, but too far out to give Saints serious concerns as Accies struggled to get forward in numbers.
They kept the fight going until the end though, mainly thanks to Cerny.
Accies looked down and out when Mensing brought down MacDonald after the forward had skipped round him in the left channel, but Cerny dived to his right to palm away Craig's 58th-minute spot-kick.
Chris Millar squandered two good shooting chances to put the game beyond Hamilton but there was no way back.
Reid, his suit soaked by a heavy downpour, showed his frustration by kicking out at an object in front of his dugout after Imrie had been penalised for a foul.
Conroy spoke to the Hamilton boss to calm him down but then riled him further by ignoring a blatant push by Michael Duberry on Imrie on the byline.
Reid's misery was compounded by news of St Mirren taking the lead at Pittodrie.
Hamilton kept going forward but, when they did work themselves into a decent position, Ali Crawford shot across the face of goal and substitute James Chambers sent a weak 30-yard free-kick wide.