The former All Blacks fly-half kicked five penalties and converted tries by James Johnston and England winger Ugo Monye.
Irish responded with two excellent tries from former England winger Topsy Ojo, with full-back Tom Homer kicking four penalties and a conversion.
The 2pm Twickenham kick-off meant that Samoan prop Johnston's 17th-minute try was the first of the new league season.
Evans had kicked Harlequins into the lead with a 40-metre penalty after only two minutes, and Homer levelled from the touchline three minutes later.
A sustained spell of Quins pressure produced the opening try.
Full-back Mike Brown was tackled a metre from the Irish line by Ojo, but Quins turned the ball back inside and launched a series of assaults.
George Robson, dominant in the lineout all afternoon, and skipper Chris Robshaw were both stopped just short before heavyweight Johnston powered his way over.
Homer missed a second touchline penalty attempt as Irish responded, when Irish skipper Daniel Bowden's superbly-weighted kick over the Quins defence produced an opportunity for young centre partner Jonathan Joseph but he was unable to breach the Quins cover.
Harlequins were temporarily reduced to 14 men when England Saxons prop Joe Marler was yellow carded by referee Greg Garner for hands in a ruck in front of his own posts.
Homer landed the simple penalty to reduce the deficit to four points but Irish were unable to exploit their one-man advantage before Marler's return.
Ojo was fortunate not to follow Marler to the sin-bin when the official decided a reprimand was sufficient after he took out the aerial Brown as the Quins man jumped for a high ball.
Despite being a man down, Quins' pressure forced another penalty for Evans.
As half-time approached, both sides squandered try-scoring chances.
Following an excellent Harlequins rolling maul, the ball flew high into the air as the charging Monye was tackled close to the Irish line.
Then Exiles flanker Kieran Roche knocked on as he tried to take Ojo's final pass one-handed following a build-up by half-backs Paul Hodgson and Adrian Jarvis.
A minute before the interval Quins lost No 8 Tom Guest - handed a start with Nick Easter away on England World Cup duty - when he was carried off on a stretcher after being injured in a tackle.
The second half was only a minute old when Irish struck back to level the scores.
Joseph fielded a kick on the halfway line and ran at the heart of the Quins defence before offloading to Ojo who raced in.
Evans restored the Quins lead with his third penalty in the 52nd minute but it lasted only a matter of seconds before Ojo struck again.
Bowden launched a diagonal run for the right-hand corner flag before slipping the ball inside to leave Ojo a clear dash for the line.
But three minutes later Evans struck his fourth penalty after Irish again infringed in front of their own posts and Quins were a point up once more.
They built on it straight away when Monye atoned for his previous miss by crashing through Homer's tackle in the left-hand corner, with Evans stroking over the touchline conversion.
A 64th-minute penalty from Homer kept Irish in touch but Evans struck his seventh goal to cancel it out four minutes later.
With two minutes to go, Homer's fourth penalty secured a losing bonus point for Irish.
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