Just before the break however his clever change of direction cross-field kick looked set to send Tommy O'Donnell in at the corner but the wing forward was thwarted by an unkind bounce.
Munster continued to dominate position and possession in the second half and Varley was again on hand to dot down in the 49th minute after Munster had opted for a scrum penalty close in rather than take the three points on offer.
Connacht then asked serious questions of the Munster defence and it required bravery and commitment form Doug Howlett and Denis Hurley to deny replacement Paul O'Donoghue at the corner flag.
Munster spent the closing minutes pounding the Connacht line in search of the bomus try but the were denied by fierce defence from the visitors.
Munster: F Jones; D Howlett (capt), C Laulala, J Downey, D Hurley; R O'Gara, C Sheridan; D Kilcoyne, D Varley, S Archer; D O'Callaghan, P O'Connell; T O'Donnell, S Dougall, J Coughlan. Replacements: M Sherry, W du Preez, BJ Botha, B Holland, N Ronan, D Williams, I Keatley, I Dineen.
Connacht: R Henshaw; D Poolman, E Griffin, D McSharry, G Duffy (capt); D Parks, K Marmion; B Wilkinson, J Harris-Wright, N White; M Kearney, G Naoupu; A Browne, W Faloon, J Muldoon. Replacements: A Flavin, D Buckley, R Loughney, M McCarthy, E McKeon, P O'Donohoe, M Nikora, F Vainikolo.
Referee: Alain Rolland (IRFU)