Despite opening the scoring, The Strongest were forced to come from behind, and only had all three points secured when Luis Melgar scored in the 90th minute at Guabira's Estadio Gilberto Parada to cap a 5-3 win.
Guabira's Delio Ojeda opened the scoring for the visitors, as he got the final touch into his own net on 23 minutes to hand The Strongest the lead.
The response from the hosts was emphatic, as they led just seven minutes later courtesy of goals to Darwin Rios and Jose Castillo.
The Strongest bounced back to lead at the half-time interval though, as Raul Castro and Victor Melgar were on target to cap a momentum-changing first-half.
The visitors would not give up their lead this time around and Pablo Escobar added to it - making it 4-2 on 66 minutes.
Rios brought up a brace, with 15 minutes to play but Guabira could not gain a point and their fate was sealed when Luis Melgar scored at the death.
The Strongest capitalised on San Jose's slip-up at Club Universitario to move second on 36 points, one shy of leaders Bolivar.
San Jose moved to 35 points with a 1-1 draw at Club Universitario but coughed up a first-half lead to drop into third.
Bolivar were untroubled in a 4-0 rout of bottom-placed Aurora, going ahead on 11 minutes before three second-half goals boosted the pace-setters' goal differential to plus-26.
Real Potosi had a 3-0 home win over Blooming, while Oriente Petrolero continued their unbeaten streak in the lead - making it five games without loss with a 0-0 draw at home to Nacional Potosi.
Wilstermann produced a late show to down Sport Boys 2-1, with Augusto Andaveris scoring in the second minute of added time to clinch three points for the hosts.
