The British No.3, bidding to reach the quarter-finals of an ATP event for the first time, squandered three match-points before succumbing to his Spanish rival 5-7 6-2 7-6(1) after an intense and gruelling battle.
Norrie came tantalisingly close to scoring a significant victory, however he stumbled with the winning post in sight. It was a physical contest that tested the fitness of both competitors, and fatigue undoubtedly contributed to the Brit's eventual demise.
Victory over Baena would have secured Norrie a place inside the Top 100 for the first time, however he is now relying on other results going his way if he is to fulfil a career ambition next week.
Baena, ranked No.77 in the world, provided Rafael Nadal with arguably his sternest test of the clay-court season so far at the Barcelona Open last week. He took eight games off the ‘King of Clay’ and is a gritty competitor.
Norrie, who impressed during his Davis Cup debut for Great Britain against Spain in February, was the more assured performer in the early stages – and he romped into a 3-1 lead after a double-fault from his rival.
It was a lead he could not sustain, though, and he became embroiled in an almighty tussle for the first set. Lung-busting rallies were frequent as the pair slugged it out from the baseline, however it eventually went the way of the dogged Brit: 7-5.
Norrie held the advantage, but his momentum was halted in the second set. The Spaniard clung on to his serve after a testing second game before establishing control and dictating matters from the back of the court.
A decider was required, and Norrie struck the first blow. The Brit moved 3-1 ahead after executing a difficult high backhand-volley to perfection. It was a moment of inspiration from the 22-year-old, and he was soon on the cusp of a significant win.
Norrie had an opportunity to serve for the match while leading 5-3, but he was unable to apply the finishing touches. A rejuvenated Baena retrieved the break, however he immediately encountered trouble as he attempted to pull level at five apiece.
The Brit carved open a 0-40 scenario on his opponent’s delivery, yet still failed to get over the winning line. On his third match-point he netted a mid-court forehand that was makeable – and it proved to be a costly error.
The tenacious Spaniard managed to force a third set shootout, and the outcome was never in doubt from the moment he collected the first point.
It was a frustrating afternoon at the office for Norrie, but he departs Portugal safe in the knowledge that his place in the main draw of Roland Garros is secure.