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That left Nottinghamshire 207 for six at tea and with their departures went any chance of getting close.
Former England man Read twice lofted the ball into the stands during a breezy, unbeaten 47 but Pakistani Tahir ran through the tail for the second time to finish with eight wickets in the match.
It was all over at 3.57pm when last man Charlie Shreck's heave spiralled a simple chance to point.
Nottinghamshire displayed their intent when Graeme Swann, sent in first to pinch-hit, found the boundary three times in the opening overs before his adventure cost him his wicket.
Swann was bowled aiming to the leg side off Mascarenhas, who then dismissed Mark Wagh two balls later by locating the outside edge, and Sean Ervive held the catch at second slip.
Lanky opener Will Jefferson took advantage of the open spaces in front of square on the off-side - Chris Tremlett bowled to six slips with the new ball - to drive several boundaries.
But it was the stroke which saw him perish for 24 on the eve of lunch when he failed to clear James Tomlinson at mid-off and handed Mascarenhas a third success.
His fourth came when left-hander Prince poked a return catch in the eighth over of the afternoon.
Hampshire ploughed on with the bat for the first 70 minutes this morning to further deteriorate Nottinghamshire's fading hopes of silverware.
England Under-19 player Dawson brought up a maiden first-class hundred as the visitors added 73 in 18 overs on the fourth morning.
Dawson, 18, bettered his previous-best score of 38 yesterday and exhibited some glorious strokes this morning on his way to three figures.
Consecutive boundaries off Charlie Shreck in the sixth over of the morning were particularly memorable - a six over extra-cover followed by a powerful off-drive.
He got to his century with a tickle off his pads from the bowling of occasional medium-pacer Bilal Shafayat.
That signalled the declaration at 449 for five with Nic Pothas unbeaten on 125.
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