Cristiano Ronaldo's opener left a sour taste for the Trotters as referee Rob Styles gave the hosts a penalty after Jlloyd Samuel played the ball when he slid into Ronaldo just before the hour mark.
Substitute Wayne Rooney also found the net for the first time this season, curling home after exchanging passes with Ronaldo.
Bolton boss Gary Megson will know his side were frustrating their hosts until Styles' intervention.
United manager Sir Alex Ferguson started with Rooney on the bench and Dimitar Berbatov and Carlos Tevez up front, but - while Tevez and Berbatov tried hard - there was no sense of a partnership between them.
The only time they were involved in anything meaningful was when they helped set up Rio Ferdinand. But the centre-half bounced his half-volley straight at Jaaskelainen.
Bolton's Fabrice Muamba was presented with the best opportunity either side had to break the first-half deadlock. He ought to have forced Edwin van der Sar into a save when Gretar Rafn Steinsson's low cross rolled into his path after Ferdinand had slid in with Kevin Davies at the near post.
But from 10 yards, the England Under-21 international was so off target his shot nearly rolled out for a throw-in.
Ferguson must have felt a bit sheepish when Styles watched Samuel what looked a perfectly timed tackle on Ronaldo, then pointed to the spot. Ronaldo stepped up and sent Jaaskelainen the wrong way.
The introduction of Rooney and Paul Scholes came not long afterwards and Rooney curled a shot into the bottom corner after a neat exchange of passes with Ronaldo 13 minutes from time.