The stylish right-handed batsman drove West Indian paceman Corey Collymore to long-on for his ninth boundary to cross Richards' record tally of 1,710 runs made in 1976.
Yousuf was unbeaten on 78 and opener Mohammad Hafeez was 85 not out as Pakistan reached lunch on 241-2. The home team now leads by 285 runs with eight wickets intact and were in a good position to take the three-match series.
Pakistan leads the series 1-0 following their nine-wicket win in the first Test in Lahore. The second Test ended in a draw at Multan.
The 32-year-old Yousuf achieved the new run record in 11 Tests, the same number it took the West Indian great.
Yousuf's 102 runs in the first innings was his eighth century of 2006, taking him past another record for the most centuries in a year, jointly held by Richards and Sri Lankan Aravinda de Silva (1997) with seven each.
When on 43 Yousuf also surpassed the Pakistan record of most runs in a three-match series set by former great Zaheer Abbas with 583 made against India in 1978.
Yousuf's feat overshadowed Hafeez's patient but valuable innings.
The opener played safe at the other end and has so far hit seven boundaries, helping Yousuf add 119 runs for the unbroken third wicket after Pakistan resumed at 130-2.
The West Indies were again sloppy in the field as Daren Ganga grassed Yousuf in the penultimate over before lunch off part-timer Ramnaresh Sarwan when the batsman was on 68.
Yousuf has so far hit 12 boundaries during his 101-ball knock and has continued as the backbone of Pakistan's batting in the series.