The Finn, who made a great early save from Chris Humphrey, stopped Steve Jennings and Michael Higdon netting just after the interval at Fir Park.
Kilmarnock were worthy of a point though and the impressive Gary Harkins hit the post for the visitors.
The goalless draw was the second the teams have played out this season but the scoreline did not reflect the willingness of both sides to attack at every opportunity.
Only some last-gasp defending and the lack of a killer instinct prevented goals coming in a lively encounter.
The point was enough to ensure Motherwell stay second in the SPL at the end of the weekend.
Motherwell started on the front foot but some sloppy passes inside their own half saw then temporarily concede the initiative and Harkins, whose twists and turns were to cause the home defence problems throughout, got a shot on target.
The hosts soon rediscovered their attacking verve. Stephen Craigan's shot was blocked in a crowded goalmouth following Tom Hateley's corner and Higdon was close to connecting with Nicky Law's cross after a slick move.
Humphrey came closer in the 15th minute when he chested down Stevie Hammell's deep cross and fired a powerful shot towards the far corner but Jaakkola got down brilliantly to push the ball just wide.
Motherwell retained an edge and Higdon shot into the side-netting after turning Manuel Pascali. Hateley's inswinging corner hit the bar before Craigan headed the rebound on to the roof of the net.
Killie cleared after a superb run and cross from Law and the visitors came back into it, with Liam Kelly shooting wide after a positive run before Hammell took the ball off the feet of Dean Shiels in the box after an incisive passing move.
Motherwell had a let-off in the 37th minute when Harkins took on Craigan inside the box and shot off the foot of the far post with Tim Clancy reacting quickly to block Paul Heffernan's follow-up.
Pascali had the ball in the net in the 43rd minute when he headed home Shiels' cross from close range but he was penalised for pushing down on Clancy's shoulders.
The second half began in open fashion and Jaakkola maintained the stalemate following an excellent move from Motherwell in the 54th minute.
The Finn came out to block from Jennings after the midfielder had played one-twos with Higdon and Keith Lasley and recovered to brilliantly block Higdon's powerful volley.
Harkins continued to cause problems, setting up Heffernan to shoot and then working space for himself, but Darren Randolph was equal to both efforts.
Hateley curled wide as both sides continued to probe for the breakthrough.
Motherwell brought on Omar Daley and Bob McHugh to freshen up their attack but they were almost exposed when clever passes from Harkins and Shiels set up Danny Buijs, but the Dutchman lacked conviction and Craigan blocked.
Buijs almost broke through again but Jennings slid in with a covering challenge.
Neither side settled for a point and Motherwell had a string of late set-pieces, while Hateley's low cross deserved a better response from his team-mates.
But a draw ultimately proved a fair result.