Fredy Guarin was sent off for his second bookable offence in the 31st minute for Colombia, who still managed to win despite striker Radamel Falcao's absence and a mistake by keeper David Ospina that gave Paraguay an early lead when a Jorge Rojas shot slipped past him in the sixth minute.
Central defender Yepes was then decisive in tilting the balance during the closing South American qualifier in Asuncion's Defensores del Chaco stadium.
The Colombia captain capitalised on a majestic free kick by James Rodriguez to score with a header past goalkeeper Justo Villar in the 38th minute. Yepes then followed up a rebound to put Colombia ahead in the 55th minute.
Colombia qualified for their first World Cup since 1998 on Friday and finished in second place in the South American group with 30 points, behind Argentina (32), and ahead of Chile (28) and Ecuador (25), who both qualified on Tuesday.
Fifth-placed Uruguay (25), despite their 3-2 victory over neighbours Argentina, will face Jordan in a two-leg play-off next month for a place in Brazil.
Paraguay (12) finished second-to-last in the group.