The European Champions, who had lost only once to Irish opposition at home since 2005, were 8-20 down at the interval after Ray Ofisa Treviranus and winger Brian Tuohy went over late in the first-half for Connacht.
That had cancelled out an early Devin Toner effort before Luke Fitzgerald went over in the second-half, ably assisted by the boot of Isa Nacewa who kicked 14 points in total.
Ian Madigan kicked a late drop goal to deny Connacht a losing bonus point as it finished 30-20 to Leinster with Willis admitting some wise words from Schmidt helped them come from behind to win.
He said: "Games against Connacht are always frantic from the first whistle. There was a fair wind out there and our backs were against the wall in the first half.
"Fair play to Connacht because they had us under a lot of pressure at times but at half-time we regrouped and clawed our way back in to the game and thankfully we managed to get the win.
"I hope that they, like ourselves, Ulster and Munster can kick on from here because we all want all four provinces to be going well come the end of the season."
Leinster remain third in the RaboDirect PRO12 standings ahead of the three-week break before travelling to Edinburgh on October 28 while Connacht move down to seventh after they were denied a bonus point.
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