Middlesex 356 and 111 for 4 (Abbott 3-24) lead Hampshire 438 (Rossouw 99, Carberry 98, Abbott 56, Ervine 53) by 29 runs
The pair produced magical and brave innings before a rare moment of ill-judgement saw them off for 98 and 99 respectively.
Despite the near misses the hosts stayed on top thanks to Kyle Abbott's evening inroads into the visitor's top-order as Middlesex ended the day 29 runs ahead.
The day began with Carberry falling two runs short of a much merited and universally wanted century after waiting since May last year to taste three figures in the Specsavers County Championship and missing the second half of last season through cancer treatment.
He watchfully negotiated the nearly overs, desperate not to gift his wicket away, after starting the day on 84. But two balls after moving to 98 with a thick edge through the slip cordon he opened his shoulders for the first time since the previous evening and edged behind leaving the Ageas Bowl in stunned silence.
Abbott, elevated to nightwatchman on the second evening, had been in flowing mood on the drive throughout the morning and reached his maiden Championship fifty off 77 balls. He had put on 80 with Carberry before the opener and Lewis McManus fell soon after each other - the wicketkeeper gloving to third slip.
Carberry's dismissal had brought Rossouw to the crease, after being forced to move down the order due to a chipped finger in his left hand. He was hit twice on the same hand twice during his counter-attacking stand with Berg with the pair adding 86 for the eighth wicket.
The pair both struck massive sixes in a speedy stand before Berg was caught and bowled by Dawid Malan, with Brad Wheal being caught behind next ball. Rossouw was inexplicably dropped by Malan in the covers when the ball barely picking up speed off the bat to loop through the fielder's hands.
Fidel Edwards, who injured his hamstring while bowling, completed a walking wounded partnership for the last wicket. Rossouw had often needed to take his bottom hand off the bat and after taking on a never-there two he was run out by Sam Robson one short of his century.
Despite a lead of 82, with the two first innings having taken until deep into the third day to complete the odds appeared to favour a draw, but Abbott had other ideas. He ripped through Sam Robson with a beauty which seemed to lift and straighten on the opener.
He then accounted for Nick Gubbins with a superb delivery, his 50th in the Championship wicket, angling slightly across the left hander to kiss the edge of the bat to second slip. Abbott almost had a third when Sean Ervine dropped a tough chance at first slip with Stevie Eskinazi on 6.
Wheal used his impressive pace to take the third scalp as Malan left a hooping in-swinger. Eskinazi and Adam Voges made a recovery to take Middlesex back into the black, but the former's late-in-the-day swipe behind for 45 off Abbott left Hampshire with a chance of making it back-to-back victories.