Ambrose made 167 and Patel 105 as the pair put on 175 for the seventh wicket to take the game away from Middlesex.
Steven Finn had taken two early wickets to keep the visitors in the game on the second morning, after they were dismissed for a below-par 167 on the opening day.
But any hopes of keeping Warwickshire's lead to a manageable level - or even forcing a slender lead - were quashed by the excellence of former England wicket-keeper batsman Ambrose and New Zealand off-spinner Patel.
Patel's second first-class century of his career was the more entertaining of the two knocks, featuring some unconventional strokes, but it was Ambrose who was the man of the day for the hosts.
Indeed, while his partnership with Patel put the Bears in the driving seat, it was his ninth wicket stand of 113 with Chris Wright (52) which really sealed their position of dominance.
By the time Ambrose was the final man to fall, Warwickshire's lead was 295, and Middlesex will need to produce a performance similar in stature to last week's win over Yorkshire if they're to earn a result from this match.