'I just turned 40, and life starts at 40 I suppose,' said Tinning. 'This is a great thrill.'
Brian Davis of England fired an 8-under 63 to finish one shot back at 18-under-par 266 along with Scotland's Andrew Coltart and Adam Scott of Australia.
Tinning played in the last group Sunday at Club de Campo. He was one stroke behind overnight leader Padraig Harrington to start the round and kept pace with a 15-foot birdie at the first. He added a birdie at the very next hole, but still trailed Harrington, who also picked up birdies on each of the first two holes.
Tinning found trouble with a bogey at the fifth, but countered with back-to-back birdies from the seventh to move to 18-under. However, he bogeyed the next two holes to drop back into an eventual five-way tie for first.
After a birdie at the 14th, Tinning knocked his third shot to four feet at the par-5 14th to join Davis and Scott atop the leaderboard.
At the par-4 15th, Tinning landed his approach inside 12 feet of the cup and ran home the putt to take the outright lead at 19-under.
Tinning's stint atop the leaderboard lasted for only one hole as his drive found a fairway bunker at the 16th. Tinning blasted out of the sand and sent his ball into the crowd of spectators and behind some trees. He scrambled to reach the green and converted a key putt for bogey.
Meanwhile, Scott birdied the same hole to move into first.
Both players exchanged positions again at the following hole. This time Tinning walked off with a birdie, while Scott dropped a shot to fall back into a tie for second. Tinning held on for par at the last and the win.
'It was hard going all day, I was very nervous,' said Tinning. 'It was lucky it was me that I came out on top because it was close all the way through the whole round.'
Tinning becomes the fourth Dane to win on tour this season, joining compatriots Thomas Bjorn, Anders Hansen and Soren Hansen.
Bradley Dredge had seven birdies, an eagle and a bogey for a round of 64. The Welshman finished at 17-under-par 267. Paul Lawrie was one shot further back at 16-under-par 268.
Harrington, who was counting on a victory this week to overtake Retief Goosen in the Order of Merit race, started well with birdies on the first two holes, but had little success from that point forward. He struggled with three bogeys on the front nine and added a bogey at the 17th to finish in a tie for seventh.
The Irishman made up no ground on Goosen, as the South African shot a final-round 67 to finish alongside Harrington at 15-under-par 269. The duo was joined by Trevor Immelman four shots off the lead.
Final results from the Telefonica Open de Madrid