Ecuador's chances of a third successive World Cup appearance already look slim after they followed up last month's 5-0 loss in Brazil with another heavy defeat.
The result, which left them at the bottom of the 10-team group with no points, prompted Suarez to resign and become the first coaching victim of the competition.
In Saturday's other game, Colombia escaped their third successive scoreless draw when Ruben Dario Bustos scored a 30-metre free kick to give them a 1-0 win over Venezuela.
Argentina struggled to break down the stubborn Bolivians for 40 minutes, before the two-time world champions went ahead when Sergio Aguero, 19, headed home his first international goal.
Riquelme then took over and signalled his intentions with a 25-metre free kick which was tipped away by Carlos Arias in the 51st minute.
Six minutes later, Riquelme took another free kick from a similar position and this time left Arias helpless as he found the top left-hand corner from 30 metres.
The diminutive playmaker followed that up with a stylish side-footed goal from Lionel Messi's run in the 74th minute.
Suarez calls it quits
Luis Fernando Suarez started saying his
goodbyes before the match even ended [AFP]
Meanwhile in Asuncion, Ecuador arrived amid reports of internal squabbling after experienced defenders Ulises de la Cruz and Ivan Hurtado were left out of the squad.
They in trouble early as Nelson Haedo Valdez and Cristian Riveros scored from corners to put Paraguay 2-0 ahead within half an hour.
Roque Santa Cruz added a superb third early in the second half and, although Ivan Kaviedes pulled one back for the visitors, Nelson Ayala and Riveros each scored for the rampant hosts, who moved to seven points.
"My decision has been taken exclusively for the good of the Ecuador team, which will surely have a better campaign without me," said Suarez, who led his side to the last 16 at the World Cup in Germany.
Colombia scored their first goal of the campaign when Ruben Dario Bustos fired in a 30-metre free kick with eight minutes remaining to sink Venezuela.
The goal unleashed frenzied celebrations at El Campin in Bogota where the crowd had been getting increasingly exasperated as Colombia pressed forward but struggled to find a way past Leonardo Morales.
Colombia, who last qualified for the finals in 1998, have five points while Venezuela, who have never played at a World Cup, have three.
The third round of matches in the two-year campaign will be completed on Sunday when Peru host Brazil and Uruguay entertain Chile.