Jambos owner Vladimir Romanov joined the New Douglas Park crowd to take in his first Hearts game since November 2007, but his side offered little attacking threat as Accies completed a perfect January with their fifth win in a row in all competitions.
Mensing opened the scoring 11 minutes in by converting a Brian Easton corner and then made it four goals in as many games with a penalty early in the second half after Robbie Neilson brought down James McCarthy.
Hearts travelled without captain Christophe Berra, who is discussing terms with Wolves after the Tynecastle club accepted a reported £2.3million offer for the centre-half.
Berra was the only change to a team which secured a late victory over Inverness last week, with Marius Zaliukas starting after his return from suspension.
Hamilton made only one change - Trent McClenahan lined up in defence in place of injured Rangers star Jordan McMillan.
Accies signalled their intentions by winning a corner straight from Hearts' kick-off, and they continued to press with a number of similar early set pieces.
Jambos midfielder Bruno Aguiar went off the field clutching an ice pack to his head after a seemingly-innocuous challenge with home captain Alex Neil - and while his side were temporarily down to 10 men, Hamilton scored.
Easton played a short corner from the right to James McArthur, who returned the pass for Easton to cross to the far post where Mensing bulleted home a header.
Hearts could have equalised with their first notable forward foray; David Obua scampered down the right wing and squared for MichaelStewart, who saw his diagonal shot touch and then roll agonisingly away from the base of the left-hand post.
Andrew Driver tried to make the most of Hearts' possession after an Aguiar free-kick from midfield was cleared, running through the defence to the right-hand side but firing over the bar from a tight angle.
The impressive Paul McGowan was prominent as Hamilton remained in the ascendancy; they also defended decisively and McCarthy delivered a delightful display of skills on the left wing from a Tomas Cerny kick-out.
Stewart had a rapid-fire chance of an equaliser on the half-hour, when he volleyed goalwards from an Aguiar pass, but Cerny made an impressive save.
There was little more goalmouth action before the break, although Obua came close with a speculative rising effort from distance, which Cerny had to touch over the bar.
Hamilton made the better start to the second half and went further in front with a penalty awarded just five minutes in.
Robbie Neilson crudely pulled down McCarthy as the youngster again demonstrated excellent footwork skills to collect Easton's flick up the left flank and work menacingly towards goal.
Mensing confidently stepped up and scored from the spot with a low drilled effort which nestled in the bottom right-hand corner; goalkeeper MacDonald went the right way but was unable to keep out Mensing's third penalty in four matches.
The visitors - under the watchful eye of Romanov - failed to mount any convincing response and could have gone further behind on the hour mark when the rising Richard Offiong was just inches away from connecting with an Easton corner.
Hearts introduced Laryea Kingston in place of Aguiar as they sought to make up ground with the game entering its final quarter.
Stewart had another chance after doing well to retain possession and unleash a snapshot from the edge of the box, but Cerny was equal to his effort and dived to collect it at his left-hand post.
Kingston then hit the side-netting after being played in on the right side of the area by Christian Nade, but Hearts never looked likely to prevent their opponents from recording a fifth consecutive clean sheet, four in a row in the SPL.
Hamilton substitute Derek Lyle almost made it 3-0 10 minutes from time with a looping header, but MacDonald claimed the effort under his crossbar.