The visitors had led by 202 overnight, and with England paceman Chris Tremlett unable to bowl after suffering back spasms the previous day, Nicholson and Ormond continued to make hay against an under-strength attack already missing the injured Shane Bond.
But after Chris Benham caught Nicholson at third man when he attempted an upper-cut off Ervine (4-42), Surrey captain Mark Butcher soon declared.
Hampshire lost Michael Carberry before lunch when he was caught behind off former West Indies paceman Pedro Collins, but Brown dropped anchor, adding 96 with Jimmy Adams (31) to give the hosts a realistic chance at victory.
Despite losing Adams and Michael Lumb, both lbw to Saqlain, Hampshire reached 123-3 by tea as Brown hit his fourth half-century in five Championship innings.
Wickets continued to fall during the chase as Saqlain removed Benham and Brown himself, while Ervine's 51 came off just 59 balls.
Captain Dimitri Mascarenhas tried to force the pace, hitting Saqlain out of the ground only to hole out at deep backward square leg the very next ball.
With the light deteriorating, seamer Ormond (2-52) turned to his occasional off-spin in support of Saqlain, claiming the vital wicket of Ervine.
All four results looked possible going into the final hour - but the chase was called off after Greg Lamb, who also hit a six, was lbw trying to reverse-sweep Ormond.
And in the end, the injured Tremlett and reserve wicket-keeper Tom Burrows batted it out for a draw.