George Naoupu and John Muldoon both won early turnovers but it was Saracens who struck first with a penalty from out-half Owen Farrell.
Matthew Jarvis' boot was called on several times in the opening exchanges and the young out-half, celebrating his 21st birthday, managed to put in some impressive clearance kicks.
Despite going down 11-0 following a second Farrell penalty and a try on the overlap from James Short, Connacht's forwards showed well in the tight exchanges.
Johnny O'Connor, Michael Swift and Jarvis all made huge hits and turned over ball with some ferocious rucking, but the whistle of referee Sean Davey did not blow Connacht's way.
The visitors found themselves 14 3 down at half-time with a Jarvis penalty being cancelled out by Farrell's third successful place-kick of the night.
A shortened half-time break due to the fading light, with both teams staying on the pitch, saw Eric Elwood's men quickly back in the thick of the action.
Muldoon, Swift, the returning Mike McCarthy and Naoupu upped it in the physicality stakes, while the back-line fired well with the little ball they received.
However, Connacht were made pay for a high penalty count and Sarries succeeded in extending their advantage. Short raced in for his second try shortly after the restart, and replacement Charlie Hodgson landed the touchline conversion.
Some slick handling from Gavin Duffy, Henry Fa'afili and Eoin Griffin left young winger Tiernan O'Halloran free to sprint in for Connacht's only, midway through the second half.
Elwood and his coaching staff will have garnered a lot from the province's three pre-season matches and getting a new squad to gel together will be seen as more important than the results.
Connacht, who travel to Benetton Treviso in their league opener next week, host the Scarlets in their first home game at the Sportsground on Saturday, September 10.
SARACENS: Alex Goode; David Strettle, Adam Powell, Brad Barritt, James Short; Owen Farrell, Neil de Kock; Rhys Gill, Schalk Brits, Carlos Nieto, Steve Borthwick (capt), Mouritz Botha, Justin Melck, Andy Saull, Ernst Joubert.
Replacements used: Charlie Hodgson for Farrell, Ben Spencer for de Kock, Deon Carstens for Gill, George Kruis for Botha (all half-time), Duncan Taylor for Powell, Jamie George for Brits, Petrus Du Plessis for Nieto, Mouritz Botha for Bortwick, Will Fraser for Melck (all 55), Nils Mordt for Barritt, Mako Vunipola for Carstens, Jackson Wray for Joubert (all 60).
CONNACHT: Gavin Duffy (capt); Tiernan O'Halloran, Eoin Griffin, Henry Fa'afili, Brian Tuohy; Matthew Jarvis, Frank Murphy; Dylan Rogers, Ethienne Reynecke, Rodney Ah You, Michael Swift, Mike McCarthy, John Muldoon, Johnny O'Connor, George Naoupu.
Replacements used: David McSharry for Fa'afili, Denis Buckley for Rogers (both 50 mins), Ray Ofisa for J O'Connor, Adrian Flavin for Reynecke (both 54), Paul O'Donohoe for Murphy (56), Thomas Anderson for Swift (60), Niall O'Connor for Jarvis (62).
Referee: Sean Davey (England)