Konate tapped in the rebound from Cheikhou Kouyate's saved header for an easy 10th-minute opener in front of 76,071 spectators at Wembley Stadium.
Uruguay's defence was left flat-footed again on Konate's second in the 37th when five defenders watched him head home a corner seven minutes after defender Abdoulaye Ba was red carded for tripping up Luis Suarez.
Konate has scored three goals at London 2012 for Olympics debutante Senegal, which leads Group A with four points from two games. Two-time Olympic champion Uruguay has three points going into its last game against hosts Britain. Senegal finishes against the United Arab Emirates.
Uruguay looked lethargic on both goals against a pacy and physical opponent, especially after the 7 1/2-hour bus ride it took from Manchester to London on Friday to take part in the opening ceremony of the games. Konate was perfectly placed inside the box to tap home after Uruguay goalkeeper Martin Campana's low, reflex save to Kouyate's clear header.
Uruguay created danger in the 27th as Gaston Ramirez's free kick bounced off the near post. The Bologna striker would later elicit a tremendous save from Ousmane Mane after Senegal was reduced to 10 men from Ba's silly trip of Suarez, who was jeered by the near capacity crowd with every touch.
Senegal struck its second goal against the run of play as Sadio Mane — who troubled Uruguay's defenders with his pace — set up a corner that Konate easily stepped up to score from as five blue shirts stood stationary around him.
Suarez set up Ramirez's try from inside the area while fellow striker Edinson Cavani was largely muted apart from having a 45th-minute effort cleared after he got free past Mane.
Uruguay defender Sebastian Coates also had a shot cleared off Senegal's goal line in an up-tempo first-half played in sunshine and showers.
Kouyate scrambled to clear second-half substitute Abel Hernandez's goal-bound shot in the 51st, but the South Americans came no closer to rallying back against a physical but disciplined Senegal, which finished with five bookings.
"We couldn't take advantage of our opportunities, we didn't manage that goal that would have maybe complicated the match for them a bit," said Uruguay coach Oscar Tabarez, whose team would travel by train to Cardiff to avoid any more planning problems. "The team ran and fought right up to the last minute. They beat us soundly."
Tabarez did not expect the treatment of Suarez — banned for eight matches last season for racially abusing Manchester United defender Patrice Evra during a match in October — to be a distraction with a finale against Britain.
Uruguay, which could have clinched the group with a victory, was unbeaten in winning back-to-back Olympic titles in 1924 and '28 — the last time it played in the competition.
Paul Logothetis can be reached at: www.twitter.com/PaulLogoAPSuggest a correction