A pair of Englishman in Jamie Spence and Gary Emerson carded matching rounds of 1-under 69 to share third place at 4-under-par 206.
Jimenez was already in the clubhouse and fellow Spaniard Olazabal was coming down the stretch in front of the home crowds with a two-shot edge at 8 under par.
Disaster struck for Olazabal at the par-4 17th, however, and the two-time Masters champion double-bogeyed the hole to fall back into a tie for the lead with Jimenez.
Olazabal had the par-3 18th remaining but found trouble again with a bogey to fall one back and lose the tournament.
'I'm obviously very happy to have won,' said Jimenez. 'But it was a surprise to me. I had finished my round and gone and had a shower and gotten changed because Olazabal was 8 under par at one point. But after I had changed into my jeans, the Tournament Director told me of the situation and I went to get ready for a playoff. I thought there would at least be a playoff but that is golf for you.'
Jimenez was five shots back after 36 holes and inclement weather forced the tournament to be cut to 54 holes. With only 18 holes left to decide a winner at Pula Golf Club, Jimenez made the most of the opportunity.
The 39-year-old tallied a pair of birdies on the front nine to make the turn at minus-3 before catching fire on the inward half.
Jimenez picked up a birdie at the 11th and another at the 12th to reach 5 under. He added back-to-back birdies from the par-4 15th to join Olazabal in the lead but dropped a shot with a bogey at the 16th.
All Jimenez could do was wait, and in the end the solid effort was enough to earn him his seventh career victory on the European Tour and his first since 1999.
'It feels great to have won again,' said Jimenez. 'My last win was at the Volvo Masters back in 1999 and it is nice to have done it in front of a Spanish crowd in Mallorca.'
For Olazabal, the disappointing finish was indicative of his season thus far.
'Just imagine how I feel right now,' said Olazabal. 'The tournament was mine when I was standing on the 17th tee but I just didn't know how to catch it.'
Simon Khan, Paul Broadhurst, Tomas Jesus Munoz, James Hepworth and Benn Barham tied for fifth at 3-under-par 207.
Klas Eriksson, Jose Manuel Lara, Miguel Angel Martin, Maarten Lafeber and Marcel Siem were one shot further back at 2-under-par 208.
David Park of Wales, who held the lead heading into the final round, struggled with a 7-over 77 to finish seven shots back at 1-over-par 211.