Former Liverpool boss Benitez took over from Jose Mourinho, now with Real Madrid, but the Spaniard's bid to retain the Champions League title won by his Portuguese predecessor did not get off to the best of starts even if there was a goal for Dutchman Wesley Sneijder in his home country.
From the free-kick which followed, Theo Janssen hit an effort from 20 yards which went into the top-left corner of the Inter goal.
An inswinging corner from right by Janssen was head into his own goal by Argentinian forward Diego Milito, who gave team-mate Julio Cesar no chance in the Inter goal.
Five minutes later Inter's Esteban Cambiasso saw his shot hit the Twente bar as the visitors pressed for an equaliser.
And Samuel Eto'o drew things level once more when he struck just before half-time. His shot from 25 yards found the bottom-right corner and gave Nikolay Mihailov no chance in the Twente goal.
Inter's Brazilian defender Maicon was shown a yellow card four minutes into the second half after he fouled Twente midfielder Nacer Chadli. Jansen tried his luck from 20 yards out but his shot was over the bar.
With 15 minutes to go Twente coach Michel Preud'homme, who took over from the departed Steve McLaren when the Englishman moved to Wolfsburg in the summer, replaced striker Marc Janko with midfielder Emir Bajrami as the home side appeared to settle for a share of the spoils.
Sneijder was Inter's most effective player as he led the visiting side's continued attempts to snatch a late winner.
With eight minutes to go Samuel's shot from the right was blocked by Bryan Ruiz as Twente fought off more Inter attacks.
Less then five minutes from the end Inter coach Benitez tried his last throw of the dice when he brought on midfielder Sulley Muntari for Samuel, but his side could not find a winner.
( ESPN.com )