Both Japan and Senagal finished on 4 points and shared the same goal difference.
Japan lost their final game of the tournament to already-eliminated Poland, although a late victor for Colombia over Senegal ensured the Asian nation progressed on the basis that they had picked up fewer yellow cards than Senegal over the course of the tournament.
Rodriguez missed Colombia's opening match due to injury, but returned to form against Poland, setting up two goals masterfully in the team's 3-0 victory.
Japan will play the winners of Group G - either England or Belgium, who were to play later Thursday - in the next round.
Japan, with 10 minutes to play of their final group game against Poland, appeared to have been made aware of the situation, after Yerry Mina headed Colombia ahead against Senegal.
For the winning team in Group G, the second-placed side from Group H will be up next, while the victor of Brazil against Mexico awaits in the quarter-final.
Senegal, who were actually leading group H at one point during their game, exit the World Cup based on picking up more yellow cards than Japan.
The centre-back, now at the World Cup with Senegal, believes the £88m (€100m) switch he is being linked with is mad.
They kept possession at the back for the remainder of the game and wasted time, despite losing 1-0, as Senegal desperately tried to find a victor. The next tiebreaker would be points earned in matches between the teams that are tied, but Japan and Senegal played to a 2-2 draw when they met in the group stage, so that was a wash as well.
"I fancy Colombia [advancing] after that performance [against Poland] - I thought they were absolutely brilliant and I like Senegal as well, but I just feel like Colombia had that horror moment in their first match getting a red card and losing that match [against Japan] and now they have a lot of momentum", TSN soccer analyst Steven Caldwell said.
While the fair play tiebreaker is far from flawless, it's likely better than what would have been the case had Senegal and Japan also been tied on yellow cards - the final remaining tiebreaker that Federation Internationale de Football Association has, in that case, is the drawing of lots.