Willem De Waal's early Treviso penalty was cancelled out by a Matthew Jarvis kick before Rodney Ah You's try helped Connacht lead 8-3 at the interval.
Another Jarvis penalty extended Connacht's lead to eight before De Waal responded with two Treviso penalties but despite an avalanche of late pressure - Elwood's men stood firm.
The Italian side were decimated by a host of World Cup call-ups - but after watching his side's gutsy away-day win - Elwood believes they're a match for any side in the RaboDirect Pro12.
"We have changed our whole approach," said Elwood. "We firmly believe on our day we are capable of challenging anybody.
"I think we have proved that home and away. The challenge this year now is can we do it again?
"Can we back it up again? Fifteen new players and that is their challenge."
Seven victories and a draw in 22 league matches last season saw Connacht finish above Aironi, Glasgow Warriors and Benetton Treviso in the table.
And Elwood is hoping for a repeat performance this time around.
"It is the start of the three-year programme," added Elwood.
"I'd like to think the work the lads did last year in the league didn't go unnoticed.
"We have 15 news guys coming in; the key for those players is to take up the mantle and build on the work that was done last year. The key word is improvement."
63x46.png){kind=logo}