Jose Goncalves sent a header against the Accies bar during a first-half during which the visitors otherwise looked the more likely side.
Michael Stewart opened the scoring from the spot when Martin Canning challenged David Witteveen in the box. Suso put Hearts further ahead with an audacious back-heel, but Marco Paixao pulled one back for Accies.
Hearts manager Csaba Laszlo had been forced into three changes from the side that defeated Dunfermline in the midweek Co-operative Insurance Cup tie.
Midfielder Ruben Palazuelos was sent home through illness, while defender Lee Wallace failed to recover from injury, meaning that David Witteveen and Ian Black were handed starting places.
With striker Gary Glen also missing out through injury, Andrew Driver was recalled after recovering from his knee problem.
Marco Paixao started up front for Hamilton after Derek Lyle was ruled out for the season last weekend.
The visitors made a confident start to proceedings as they had Hearts pegged back in their own half, but it was the Tynecastle outfit that conjured the first chances but both Suso and Witteveen failed to make contact in front of goal.
Accies created their first opening in the 15th minute when Janos Balogh's attempted clearance fell to Paixao, but the ball ricocheted off the Portuguese player's legs and fell wide.
Hearts' David Obua should have done better with a free header from Craig Thomson's corner after he missed the target from close range. Goncalves then powered a header off the bar in the 33rd minute after connecting with Thomson's out-swinging corner and Ismael Bouzid was out of reach of the follow-up as he tried to net the rebound.
Stewart gave away a free-kick 20-yards from goal after clattering into James Wesolowski and Hastings' free-kick was deflected just wide of Balogh's goal.
Hamilton finished the half the stronger as Antoine-Curier then blasted wide after latching on to Simon Mensing's through pass.
Just three minutes into the second half, Suso looked to make an impact with a curling effort from the edge of the box, but Tomas Cerny pulled off a fine diving save.
Hearts took control of the game with two goals in as many minutes that left the visitors shell-shocked. The first arrived in the 55th minute through Stewart from the penalty spot. The midfielder played a quick free-kick to Witteveen and the Austrian was adjudged to have been fouled by Martin Canning after rounding the defender.
Stewart made no mistake with a clinical shot into the corner and the home side then doubled their lead minutes later courtesy of Suso.
Thomson's corner was headed down to the winger by Bouzid and Suso back-heeled the ball over the line right in front of the goalkeeper.
Hamilton winger Paixao reduced his side's arrears in the 62nd minute. The midfielder nipped in to collect Grant Evans' pass ahead of Marius Zaliukas before applying a cool finish from close range.
Despite the disappointment of losing a goal to their opponents, Hearts continued to press as they looked to put the game beyond doubt. Hearts brought on winger Arvydas Novikovas for goalscorer Suso and the Lithuanian winger was in the thick of the action right away. The hosts had claims for a penalty waved away by referee Alan Muir after Novikovas fell in the box under a challenge from Hastings. Moments later, Novikovas created space on the edge of the box, but he dragged his shot wide.