Shah, at the helm while Andrew Strauss is on England duty in the Caribbean, and Ben Hutton (88) shouldered the burden of seeing Middlesex to their potentially tricky target of 297 on the fourth and final day of their first division match.
The victory was Middlesex's first championship win over their neighbours since 1995 but it was never in doubt as every batsman made a contribution to the win.
Shah, who made 93 in the first innings, put on 108 for the second wicket with Hutton, who made his second half-century of the match before being caught behind to Saqlain Mushtaq.
Nottinghamshire opened their Division Two campaign with a convincing win over perennial strugglers Durham, who were routed in double-quick time at the Riverside.
Resuming on 30 for three they collapsed to 93 all out to hand Notts, relegated from the top flight last season, victory inside an hour and a half.
Charlie Shreck finished with six for 46, taking nine wickets in the match, with fellow seamer Greg Smith claiming three for 28.
Graeme Bridge top scored with 17 off 25 balls but it was not enough to stave off defeat by an innings and 80 runs.